"Verification failed: your Apple ID or password is incorrect" - and it's not - how to fix?

My daughter is having problems with her iPod touch. Some of her apps (not all) are asking for my Apple ID password instead of hers in order to complete updating. (We have Apple Family Sharing switched on so I guess it might be something to do with this.) When I try to enter my Apple password for her, it tells me it's incorrect (it's not).

Is there any way round this that doesn't involve deleting the apps in question and reinstalling them? She has game progress saved in some of them that she really doesn't want to lose. Thanks!