Pokemon-go – Will I be able to re-enter the Pokemon Go account after downloading it on another Apple ID

Yes, all game data is stored on an online server. I tried this myself two days ago.

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.