In reading the dissertation by J. William Goldsmith, "The Competence of Church and State of Marriage - Disputed Points", published by Catholic University Press, 1944, I find:

ARTICLE 2 [page 20]

THE JURIDICAL RELATIONS OF CHURCH AND STATE WITH REGARD TO 'REX MIXTAE'

In a general way the relations of the two species of perfect society have already been indicated.  The indirect supremacy of the Church over the State by reason of the superiority of aim and purpose inherent in the former has been pointed out; a somewhat more specific indication of their relations has also been furnished in the treatment o their respective functions.  Now there remains to be demonstrated the particular aspect of their juridical relations which is fundamental to the solution of the problems of competence that constitute the object of this study.

A. DEFINITION AND DIVISION OF "RES MIXTAE"

1. Meaning and Extent of the Term:
     Things may be considered as being of a spiritual, temporal, or mixed character.  This designation is to be understood not ontologically but finaliter, I.e., from a consideration of their inherent ends or acknowledge purposes.  Thus, spiritual things are those which, although material in themselves, exclusively tend or are ordered to a supernatural end.  Temporal things are those that, even though they be not material in themselves, are ordained to a temporal end. (note Coranata, op. cit., n. 83) Things of a mixed character (res mixtae) are those which are directly referred to a twofold end, scil., spiritual and temporal, and according to either respect are under the disposition of the competent society. (note Ottaviani, op. cit., II n. 325) [transcriber's' note, the two societies are Church and State]  Hence there is a distinction between the notion of res mixtae (things of a mixed character which directly tend both to a spiritual and to a temporal end) and the notion of res mixti fori (issues which in their character are concurrently subject to an equal competence exercisable by the Church and State  alike).  The former concerns the competence of both societies over the same matter but under different aspects.  In that case Church and State are both interested in the matter, not in a cumulative but rather in a discrete manner. Res mixti fori, however, are those things in which Church and State have a cumulative power in such wise that whichever society takes up the matter first has the right to go through with it.
    Res mixtae in the strict sense are those which of their nature, by virtue of their natural quality and purpose, directly tend to both ends at the same time.  In the broad sense, the concept of res mistae includes those things which themselves tend directly to only one end, but which through some added quality are ordered to the good of the other society also. (note Ottaviani, op. cit., II, n. 326)

2. Classes of "Res Mixtae":
     A rex mixta can be such either of its very nature or through a process which supernaturalizes its otherwise temporal character [end page 21] or purely material content.  The former (res mixta naturalis) while it remains within the limits of the order of nature, nevertheless is an object to which attaches a spiritual as well as temporal import.  When this category, for example, would lie a marriage that is not endowed with the sacramental character.  A res mixta which becomes such by being supernaturalized is one which by a positive act has been elevated to a higher order, to the supernatural order; such would be marriage raised to the dignity of a sacrament.  A third class is sometimes distinguished as a res mixta supernturalis. But a res mista supernaturalizata and a res mixta supernturalis are usually assimilated one to the other, for with regard to the question of competence they are both governed by the same juridic principles. (note Cf. Coranata, op. cit., n. 87; Ottiviani, op, cit, II, n. 327 and note 5: Cappello, op. cit., I, 222.)
     Finally, there must be noted the two classes of effects possible to supernaturalized or supernatural matters of mixed character.  Those effects which flow necessarily from the supernaturalized thing, and are so bound up with it that they can in no wise be disjoined therefrom, are called inseparable.  Such inseparable effects cannot be make the subject of negotiation without at the same time having the substance of the thin to which they are annexed touched also.  Two examples in point are the spiritual and supernatural graces and helps that necessarily proceed from Christian marriage, and the juridic condition of legitimated offspring.  On the other hand, those effects which do not necessarily derive from the substance of res mistra and are not unchangeably connected with it, but rather depend upon the command of positive law and therefore can be disjoined from the thing itself, are called separable.  Moreover, when these separable effects are temporal, they are given the name of merely civil effects.  (note Ottaviani, op. cit., II, n. 327) [end page 22]

B  THE JURIDICAL PRINCIPLES GOVERNING "RES MIXTAE"
    " Having in mind these concepts of the different kinds of res mixtae, and considering the notions of perfect societies as previously [end page 22] set forth, one can establish certain definite juridical principles that must necessarily govern the power of such societies over matters that lie within the sphere of res mixtae. one may treat of these principles by attending first to the more general and then to the more particular divisions of matters or objects which are of mixed character.
     "In the first place, with regard to such matters, of whatever kind they be, civil society cannot make laws by prescinding from related ecclesiastical legislation; but it is the duty of the Church and the State to legislate by mutual agreement, safeguarding always the superior claims inherent in the Church as a society of higher order. (note Cavagnis, op. cit., I, n. 423; Cappello, op. cit., I, 223; Ottaviant, op. cit., II, N. 328)
 "This principle follows from the fact that according to the designs of God the two powers to which He has committed the care of the human race should work together in harmony and concord for the attainment of their respective ends. (note Leo XII, ep. enccl. Immortale Dei, 1 nov. 1885, §6--Fontes, n. 592.) The Church, it is true, has by reason of its existence as a society of a higher order the prevalent right in a question of res mixtae.  But she has always recognized a certain duty of negative justice that binds her to give consideration to the prior and just legislation of the State, and not to hinder without necessity the operation of such laws.  The State, on the other hand, has a corresponding obligation to respect the canonical legislation on such matters: not to prohibit what is prescribed by canon law; and not to impose on their mutual subjects what is forbidden by the Church (note Cavagnis, op. cit., I, n. 424.)  If this duty to legislate by mutual agreement were faithfully attended to much difficulty would be avoided.  But when these two societies function separately and enact laws that prescind one from the other, conflict of legislation can and does easily arise.  And here in the event of conflict, the State, being the inferior society, must give way to the higher authority of the Church.
     "The second principle bay be stated thus:  As regards both the [end page 23] matters of a mixed character which are such of their very nature or essence, and also the effects which derive therefrom, each society can make laws that pertain to its own proper end. (note Cavagnis, op. cit., I, n. 426; Cappello, op. cit., I, 225; Ottaviani, op. cit., II, n. 329.)
 In these matters, then, each society may exercise its power over this aspect which pertains to its own proper end in the spiritual or in the temporal order, provided again that in case of conflict there be safeguarded the superior claims of the Church over the State.  The first part of this proposition follows from the independence which each of these societies enjoys; and the proviso is a corollary of the indirect superiority that the Church has demonstrated over the State.
     From this principle it is evident that a thing which of its nature is of a mixed character, even though it tend directly unto a spiritual end, does not by that fact lose its place in the order of nature as a thing ordained to a temporal end also. Hence the fact that instruction given to children in schools [ ...
... ] Another [end page 24] example of a matter which of its very nature is of a mixed character may be found in marriage that has no sacramental character, as, e.g., in a marriage between two unbaptized persons.  Prescinding from the question as to whether the rights over such a marriage belong to the State ex iur proprio et ativo or only ex iure devolutivo et hypothetico, one must advit that the State is recognized to have certain rights over such a marriage; but her rights therein are by no means exclusive, for marriage even as a natural contract has a sacred character.  Indeed, radically and fundamentally it is that very sacredness that places the power to dissolve the bond of marriage outside the competence of the State.
     A third principle governing res mixtae concerns those that are either supernatural or supernaturalized.  The civil power can make no disposition with respect either to the substance or to the inseparable effects of supernatural or supernaturalized "res mixtae"; but the power of the State extends only to the merely civil (i.e. separable and temporal) effects of these things, the while it must preserve the proper subordination to the ecclesiastical law. (note Cavagnis, op. cit., I, nn. 428-432; Cappello, op.cit., I, 225-229; Coranata, op. cit., n. 87; Ottaviani, op. cit., II, n. 330.)
    The reason for this is that such things are in and of themselves spiritual; this spiritual quality belong to them either of themselves as supernatural things, or by their elevation to a higher order whereby they have become endowed with the nature of supernatural things.  It is, therefore, only incidental that they have some temporal effects; and , consequently, it is only in a broad sense that they may be called matters of a mixed character.  Since the Church alone has competence over things essentially supernatural, it is evindent that she alone has full power over the substance o things that are supernatural or supernaturalized.  The same is true in regard to the inseparable effects of these things, for, as has already been shown, such effects are intimately connected with the substance and follow its nature according to the principle assenssorium sequitur principale.  And therefore, that power which is competent to take cognizance of and to [end page 25] make regulations concerning the cause, it belongs also to dispose of such effects as are necessarily connected with the same cause. (note Ottaviani, op. cit., II, n. 330)
     Concerning the merely civil effects, the State, it has been noted, can legislate provided that these civil regulations be not opposed to the laws of the Church.  It is obvious from the definition of separable temporal effects that they are directed to the end which is proper to civil society; moreover, they do not derive from the substance of the thing and are not inseparably linked to it.  Consequently, by nature they fall within the sphere of the temporal order and are subject to the power of the State.  That competence over these temporal effects must, however, be exercised with moderation and with due regard for the spiritual substance from which they flow and over which the Church has full power.  If, therefore, an unjust law is enacted by the State in such matters the Church can exempt her subjects from that law; and even if the law be useful from the viewpoint of civil society but is in any way harmful to the spiritual good, the Church again can exempt her subjects from its observance.
   As an example of the supernatural res mixtra one can point to baptism; by reason of its divine institution as a sacrament it lies outside the competence of the civil power which exists within the temporal order, and which, accordingly, cannot exercise its jurisdiction over a thing in the spiritual order.  The State, then, could never settle the question of the validity or invalidity of the administration of baptism; but if a question of inheritance turned upon the baptism of some individual, the State could decide a point of bare fact as to whether baptism as a ceremony had or had not been administered to that individual.
     The contract of marriage through its elevation by Christ to the dignity of a sacrament is in the class of supernaturalized res mixtae.  Its substance is supernaturalixed and consequently is wholly subject to the power of the Church.  From such a marriage there flow certain effects which have intrinsic and necessary connection with the substance of the thing,  and are inseparable from it.  Such effects are, for example, questions concerning the freedom of the parties to contract marriage, the [end page 26] unity and indissolubility of the marriage bond, the legitimacy of offspring, etc.  And, as previously pointed out, concerning these effects the Church alone is competent to make laws and pass judgment.  THere are other effects that are connected only incidentally with the substance of the matrimonial contract, and are, in consequence, separable from it.  Among such effects are the rights of succession in regard to nobility or in regard to property, the rights to share in an inheritance, dowry rights, etc.  The State can make laws establishing certain conditions to be fulfilled in order that these effects may follow legally--provided, as always, that these conditions are not contrary to divine or ecclesiastical law.
   In all questions concerning res mixtae, then, there should be preserved the fundamental competence of Church and State, each in its own proper order; and in the vent of conflict the indirect superiority of the Church, must, because of its higher aims, prevail.  In conclusion, it may well be noted that the tendency of the Church has been clearly indicated by her insistent and repeated pleas for the maintenance of that harmonious union which should characterize the relations of the spiritual an the temporal authorities.  For, as Pope Leo XIII has observed: "... in such arrangement and harmony is found no only the best line of action for each power, but also the most opportune and efficacious method of helping men in all that pertains to their life here, and to their hop of salvation hereafter." (note Ep. encycl. Arcanum Divinae, 10 feb. 1880, §22--Fonte, n. 580; English translation from the Pope and the People (London: Catholic Truth Society, 1937), p. 40.) [end page 27]
 

In reading the dissertation by Reverend James Patrick King, "The Canonical Procedure in Separation Cases" published by Catholic University of America, 1952 I find:

"One cannot deny that the ecclesiastic judge may decide matters relating to the 'so-called' civil effects of marriage, such as property settlements and payment of alimony.  Although these matters may not be explicitly res spirituales as are the separation suites themselves, never-the-less, they pertain to it most intimately ex conexione causarum, and the ecclesiastic judge is canonically compentent to adjudicate them. (note cc 1553) (page 109)

"The matters of support of the separated wife and custody of children are of paramount importance.... Relative norms for [deciding custody and support] may be found in Decretal Law. (note C. 1-8, X, de donationibus inter virum et uxiroem, et de dote paost divortium restituenda, IV, 20.) (page 111)