You can share an Apple ID and use multiple devices with one iTunes library. I have multiple devices and use one iTunes library and each device has its own content on it.
If you want to restore all of your app data and device settings to the new iPad - and that IS what you want to do - you want to restore from a backup. I assume that you were sharing this iPad with your wife and all of you games and apps are on it as well, so I assume that the iTunes backup has all of your game scores and app data in it.
If you use iTunes for the backup, restore from the iTunes backup, and then sync with iTunes in order to transfer all of your apps, photos, movies, books and other media onto the device.
You can read this for more help. This article explains how to do it, but when you read the part about choosing your own playlists, that applies to all of the iTunes content in your library. You can select the unique content that you want to sync to each device.Essentially, you want to use Method Two in your case.