Why am I getting my wife’s text messages?

Immediately stop sharing an Apple ID. Each person, regardless of age, needs her/his own, unique Apple ID.

The person obtaining the new Apple ID must thoroughly cleanse her/his Apple device(s) as follows before “moving in”:

What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support

She must not change an Apple ID as that would change your Apple ID.

She must create a new Apple ID…

How to create a new Apple ID - Apple Support

… and thoroughly cleanse her iPhone as follows before “moving in” using that new ID:

What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support

yankeecause wrote:

We don’t share an Apple ID. She doesn’t use one.

That is not possible - assuming she uses an iPhone.

OK, sounds like a good idea if you’re stuck.

Good luck!