App Store Asking to Sign in with Incorrect ID

When trying to update all non-uninstallable apps (iMove, Key Note, Numbers, etc) on my MacBook Pro, iTunes/App store is requiring I sign into an apple ID I do not have access to instead of the one that it is already logged in to. The old apple ID is one I have previously used back in the iPod Touch days and no longer have access to the phone number attached to the two-step verification, but do have its password. No one who has previously used that login uses it anymore.

I have tried logging out and logging back into the App Store using the *correct* ID, updating the operating software, and rebooting my computer with no luck. It tries to log in with the wrong ID, and when I type in the correct ID/Password, I get this error, which will loop in perpetuity until I click cancel. This effectively makes my computer one really expensive internet browser, which is both a waste of money and time as I purchased this computer to use creative apps. Help!