Brianpck says in his answer here that in Latin, attributive adjectives that semantically refer to multiple coordinated nouns tend to agree in gender and number with the closest noun, rather than with the number and gender of the total combination (the latter strategy is called "resolution").
I would therefore advise against the wording "Mei Uxor animusque". I'm not sure whether it would be outright ungrammatical, or just a dispreferred pattern of agreement. I found a dissertation that implies that resolution was categorically avoided for attributive adjectives in Latin: "Attributive targets always show Nearest Antecedent Agreement", p. 65 in "Deconstructing and Reconstructing Semantic Agreement: A Case Study of Multiple Antecedent Agreement in Indo-European", by Cynthia A. Johnson, 2014.
I believe "Mea uxor animusque" would be grammatical and could convey the intended meaning; I'm not sure about the details of word order and the use of -que vs. et. With a different word order, the possessive adjective might take a different form according to this rule (e.g. Uxor animusque meus).
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/