How do I change my iPads FaceTime phone number?

Settings > FaceTime; You can be reached for calls at:

I think it has to match a phone number assigned to an iPhone on the same Apple ID. Did your iPhone change numbers, or are you switching to a different iPhone with a different number?

If your wife's cell number was listed on the iPad, you must have set up the iPad using her iCloud account (Apple ID) instead of your own. iCloud automatically populates the phone number to other devices with the same iCloud account, but you should be able to deactivate it.

That number that is assigned to your iPad is just an internal routing and billing number for your carrier. My carrier (AT&T) makes a clear statement in the legal documents that this number is not for phone calls or (SMS or MMS) messages, just for data delivery. For whatever reason, Apple does not allow it to be used in the iMessages system.