Pokemon-go – Why can’t I use another google account on the phone for Pokémon Go

As long as you are using different google accounts for Pokemon Go the fact that you are using the same apple ID will have no impact whatsoever on the game.

If you have changed Apple accounts since you downloaded the app then you may run into a problem when the app updates as it will ask for the password of the account is was downloaded under.

You can simply delete the app and redownload it under your current apple ID in order to have it under your current Apple ID instead of the old one. The fact that two people are using the same apple ID won't have any impact. It only matters that you have changed it since downloading it.

I suggest you try deleting pokemon go's chache or app data before reinstalling, or even unlink your google account as well, and link it back in the dialog you get when you click sign in with google without having an account linked already.

If you don't know how to do those, post your phone model in a comment and I'll try to guide you into doing those.