Hello altor77,
Thanks for using the Apple Support Communities!
I understand that your wife recently changed her Apple ID to a personal email address and is now prompted for the old Apple IDs password while attempting to update apps.
Did your wife create a new Apple ID or edit the old Apple ID as shown in the following article?
Change your Apple ID - Apple Support
If the Apple ID was edited and changed to the new email address, all your wife should need to do to update apps is sign out of the old Apple ID and sign in to the new one. These steps are located in the iTunes, iBooks, and App Store section in the article below.
Sign in with a different Apple ID on your iPhone, iPad, or iPod touch - Apple Support
Other information about what to do after editing an Apple ID or changing your Apple ID password can be found in the following article.
What to do after you change your Apple ID email address or password - Apple Support
If your wife created a brand new Apple ID, it would make sense why the old apps are asking for that account information. Purchases, even free downloads, are directly tied to the Apple ID that originally downloaded them.
To resolve this issue, there are two choices:
1. You (your wife) can download these apps again fresh with the new Apple ID so they will now be associated with the new account
2. You (your wife) can sign out of the current Apple ID for iTunes & App Stores as described in the above article and sign into the old one. After signing into the old one, the apps should be available to update. Once updated, sign out of the old Apple ID and then back into the new, correct one. This process will have to be repeated any time there are new app updates with apps that are associated with the old Apple ID.
Cheers!