You and your wife should use separate Apple IDs and keep your devlices synced using separate iTunes. You should start your iPad with a clean slate by doing Settings > General > Reset > Erase all content and settings.
You should also make sure before doing that it's signed out of FaceTime and Messages (in Settings).
Then, once you set up your iPad as brand new, you can get your wife's apps by moving them into your iTunes on your computer, having her do Store > Authorize This Computer on your machine using her Apple ID and password, then sync them to your iPad.
Sync Your iOS Device with a New Computer Without Losing Data
Syncing to a "New" Computer or replacing a "crashed" Hard Drive
How to use multiple iPods, iPads, or iPhones with one computer
How To Best Use and Share Apple IDs across iPhones, iPads and iPods