When you first started the iPad Air and began to use it, what did you do? Did you restore it from a backup? If so, did that restore happen from iCloud, or from a computer? If it was set up new, did you at any point put in the ID from your wife?

The two apps that are showing in the update screen for whatever reason are bound to your wife's ID. Deleting the apps, and redownloading them should bind them to your ID. to fix the current issue. Knowing more about what path you took to setup the iPad will help reveal why the Air thinks it needs your wife's info.