How do I separate my wife’s phone recents from those on my phone

Stop sharing an Apple ID with her.

To Apple's systems, you are one person with 2 devices.

Check Family Sharing for Apple's solution to sharing most iTunes content while having privacy.

https://support.apple.com/en-ca/ht201060

You would sign out of her Apple ID in all settings on your phone. iTunes, iCloud, Messages, FaceTime.

Then using your own Apple ID, sign back in to the same settings on your phone.

If you whis, follow the steps in the article for Family Sharing.