I have an iPhone 7 and my messages are appearing on my wife’s phone and iPad, how can I stop this from happening and just have her messages going to her phone and iPad?

Why family sharing? You can set up family sharing to share app purchases and other details and other services with other family members, and which is the usual reason folks try to use one Apple ID across multiple devices.

Wiping the device was described in the previously-attached link—the blue text shown around here is a link, click on that to view the linked articles—and the sequence necessary here to switch from one Apple ID and Activation Lock and the other details over to another Apple ID is basically the same as preparing the iPhone or iPad for sale or for giving away.

What you're seeing here is expected and normal behavior, when an Apple ID is shared.

An Apple ID is per-person.

To do what you want here, create or use another Apple ID, wipe and reload the iPhone to select that other Apple ID, and then set up family sharing.

Changing the associated Apple ID is effectively the same as this:

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

Then set up Family Sharing - Apple

And if needed: How to create a new Apple ID - Apple Support

If you are sharing an Apple ID one of you needs to create their own and not do that.