App store (OSX) asking for wrong Apple ID

Switch to the Featured tab and click the Account link. Now you can sign in with the correct Apple ID. After a successful login, switch back to the Updates tab and try the update again. It should recognize that you're already logged in and continue without prompting for the wrong Apple ID password.

This seems to be a bug in the App Store. Mine always asks for my daughter's Apple ID. No reason why it should. I need to use this workaround every time I update my apps.

Thank you!
You're the only one who actually gave a helpful advice.
Others keep saying "it's just because another user downloaded the app you're trying to update", which is never the case.
Hope they'll get rid of this bug in High Sierra.

Well done - this is the actual answer to the question. Thank you.

See NotARealDoctor's answer. APPLE PAY ATTENTION. Correct this issue. It is a BUG.

What you have to remember is that Apps installed with an Apple ID are forever tied to that ID. The same goes with your updates, they too will need the original ID.

So the question is, while you could forego whatever you have now, could you then create a new ID and keep a record for future use by whoever?

I'm not sure how dangerous that may be in such an environment. Why don't you call the UK Apple Support number and ask to speak to their security team. They would be the people to advise you how to best meet these circumstances.

You need to erase all content and settings to bring the iPad to factory settings. You need to create an Apple ID that you control for the iPad that your share with the user, but that you can change the password for if the iPad is passed to another user in the future.

Not sure why I thought it an iPad.

Use OS X Recovery to erase and reinstall the OS. Restart and press & hold Command + R.

I had the same problem and I went into the Applications folder and trashed the App in question then went back to the app store and installed it with the right Apple ID. That seemed to work.