Switching Apple ID on iPad (without losing progress)
I think most people worry about this when they stop sharing an iPad. I used to hear these concerns all the time at the AASP I worked at. Let's address each issue in turn.


Apps will still remain associated to your mom's Apple ID, but they won't disappear. If you sign out of your mom's account and sign in with the new one, the apps stay exactly where they are. The only snag is, when it comes time to update, you will be asked for your mom's Apple ID and password to update them.
None of the data saved in apps will disappear when you switch an Apple ID as it is all saved locally on the device (except in the case of online games such as Clash of Clans etc, but they usually require you to log in with a 3rd Party service such as Facebook which then stores your save data instead).
Unfortunately, the Game Centre achievements are linked to your mom's Apple ID and if you sign out of hers and in with another, those achievements will disappear. Often, games feature a local achievement board which will remain on the device, and there is a chance it would sync to the new Apple ID, but in most cases I'm afraid you'll have to get those achievements again. But hey, look at it this way, that old game you haven't played in months? You can have some more fun with it again trying to set your old high score! ;)


You can have a look at another post of mine here where I talk about backing up and restoring save games on an iPad when switching users. You can use the information in there to backup your saves, then delete the games and re-download them with the new Apple ID to circumvent the annoying need for your mom's Apple ID whenever they need to be updated.

Obviously, any purchased apps and games would need to be re-purchased if you do this, so I would recommend your mom enable Family Sharing on her Apple ID and add the new Apple ID to the family so you can access her purchases without paying for them again.