On the
iPad, Settings->Messages->Send & Receive, there should be a list of phone numbers and email addresses that are allowed to send Notifications to the iPad. I suspect you will find your wife's phone number and most, if not all, her iCloud email addresses. You can remove the the phone number by tap & hold. That should remove the check mark but it will leave the number for use if your wife changes her mind. It might be nice to have your phone number listed there (with a check mark) but I'm uncertain how to do that at the moment.
The advantage of having the ability to use the iPad to use the phone is to supposedly avoid using your phone's minutes.
