Why do SMS messages addressed to me also go to my wife. I also get messages addressed to her. We both use iPhones and have an Apple Mac which also connects to iCloud.
If you are both using the same Apple ID then it is most likely 'Text Message Forwarding', a feature of Continuity in iCloud.
To disable this, go to Settings > Messages > Send & Receive and turn un-tick any other numbers that aren't yours.
Also, go to Settings > Messages > Text Message Forwarding and ensure it is turned off for any devices you don't want your messages showing up on.
Alternatively, look into setting up Family Sharing so that you and your wife can both have separate Apple IDs.