Pokemon-go – Do traded Pokemon count as caught Pokemon

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 have a similar problem, in my case it is my gmail account and I was level 10 in-game.

According to an article on Polygon, the 1.0.1 update to Pokemon Go for iOS is to blame for locking people out of their Trainer Club accounts:

Pokémon Go is reportedly locking users out of their Pokémon Trainer Club accounts, following an update for iOS users. According to members of Reddit, along with those of us at Polygon, the latest version of the game is locking out players who use their Trainer Club logins to access the game.

To fix your issue, you should update Pokemon Go to version 1.0.2:

Update: Niantic Labs has released an update for Pokémon Go on iOS that fixes the Trainer Club login issue. Version 1.0.2 is now available to download and will allow players with Trainer Club accounts to log back into their accounts.