The problem comes from the fact that you and your wife are using the same Apple ID. One of you will need to create a new apple id, and then use this on a phone. Once you've created the new Apple ID, on the phone that you will use this new id, go to Facetime and tap the apple id and select log out. Then turn off facetime (if is it hasnt turned off itself already) and then turn off imessage.
Restart the phone
Once the phone is running again, go to Facetime and turn it on. It should now ask you to log in to your apple id, if it happens to prompt for the old account, select other account, and submit your new Apple Id and password. If it doesnt prompt the old account, then just submit your new Apple Id and password.
It will activate using this new account. While this is activating, go to iMessage and turn on iMessage and it will also activate.
Note just becuase you use a different account for facetime and iMessage, does not mean you can't share apps with one apple id. You can you just need to go to the iTunes and Appstore settings, under setttings, and supply the original Apple ID inforamtion there.
Hope this helps!