Usually an adjective (and here meus works like an adjective) takes the form of the closest referent when used attributively.
The masculine plural would be used in a sentence like "the wife and soul are mine".
I find it better to put the adjective at the end, which would give you uxor animusque meus.
If you don't want to use anima instead of animus (they mean different things), there will be both a masculine and a feminine, and I find it a little awkward to refer to a wife with a masculine word even if grammatical.
Swapping the word order is one way around this, giving animus uxorque mea.
I prefer this also because of more balanced word lengths.
Another option is to use mihi, "to me".
If I may take some liberties, I suggest [tu/es] animus uxorque mihi, "[you are] the soul and wife to me".
Whether you want to include tu or es or both is a matter of taste.
On a quick thought, I would go with es animus uxorque mihi.
Before making a choice here, I suggest waiting a day or two to see if others have other suggestions or if their comments or votes suggests that mine is not to be trusted.