The use of the masculine plural "Mei" in "Mei Uxor animusque" would not follow the preferred pattern of adjective agreement in Latin. When an attributive adjective semantically modifies multiple coordinated nouns, the adjective agrees as a rule with the gender and number of the closest noun, not with the number and gender of the total combination (the latter strategy is called "resolution"). See Brianpck' answer to a related question and the dissertation "Deconstructing and Reconstructing Semantic Agreement: A Case Study of Multiple Antecedent Agreement in Indo-European", by Cynthia A. Johnson, 2014: "Attributive targets always show Nearest Antecedent Agreement" (p. 65). Pinkster 2015:1273 gives a few examples of exceptions,* but says "It is much more common for the modifier to agree with only one of the members of the compound noun phrase, almost always with the nearest one".
Alternatives consistent with this rule would be "Mea uxor animusque", "Uxor animusque meus" or "Uxor mea animusque".
Hoere is an informative forum post: https://latindiscussion.org/threads/agreement-of-an-attribute-with-more-than-one-noun.32219/
The user Bitmap (Apr 16, 2019), citing Ausführliche Grammatik der lateinischen Sprache by Kühner & Stegmann (1914), presents the main options as follows:
An attribute (adjective, participle, pronoun) that refers to more than one noun usually agrees with the nearest noun, but refers to the other nouns as well; it does not matter whether they have the same genus and numerus or not. You find the following possibilities:
a) The attribute precedes all nouns.
E.g. Caes. B. G. 5, 11, 5 res multae operae et laboris.
6, 42, 2 ab ipso vallo portisque castrorum.
Cic. Tusc 1, 7 Aristoteles, vir summo ingenio, scientia, copia.
b) The attribute comes after all nouns.
E.g. Cic. de or. 2, 242 ingenuitatem et ruborem suum.
Rpb. 1, 51 divitiae, nomen, opes vacuae consilio.
c) The attribute comes after the first noun.
E.g. Cic. de or. 3, 82 vitam tuam ac studia.
97 et ingenia vestra (...) et aetates.
98 fastidio quodam et satietate.
Caes. B. G. 3, 5, 2 vir et consilii magni et virtutis.
An attributive adjective coming between two nouns and agreeing with the second seems to be rare or unused in prose, but occurs in poetry:
In poetry, this way of positioning attributes can be found often and usually presents a figura ἀπὸ κοινοῦ (apo koinou), i.e. the attribute refers to both nouns.
E.g. Ov. her. 5, 39 consului (...) anusque longaevosque senes.
Verg. A. 2, 422 primi clipeos mentitaque tela agnoscunt.
Hor. C. 1, 5, 6 heu quoties fidem mutatosque deos flebit.
It is also grammatical to repeat the adjectives. The post also mentions that
In some cases the attribute may refer to the more distant, but more important noun.
E.g. Cic. Fin. 5, 18 prima quasi virtutum igniculi et semina.
A discussion on agreement of predicative adjectives can be found here: https://latindiscussion.org/threads/agreement.4137/
*Pinkster cites the following rare examples of attributive adjectives showing resolution:
- (a) Eo domum, patrem atque matrem ut meos salutem.
(‘I shall go home and pay my respects to my father and mother.’ Pl. Mer. 659)
- (b) Haec ea aestate . . . ab consule et legato Romanis ... gesta.
(‘These things were accomplished this summer by the Roman consul and lieutenant.’
Liv. 31.47.3)
- (c) Prolataque Divorum Iuli et Augusti diplomata ut vetera et obsoleta deflabat.
(‘And when discharge certificates of the deified Julius and Augustus were presented to him, he waved them aside as old and out of date.’ Suet. Cal. 38.1)
(Harm Pinkster, The Oxford Latin Syntax, vol. 1: The Simple Clause, Oxford University Press, §13.21, page 1273)