Being asked to log in to a different account to update Mac App Store apps
When you install Apps, you usually install them to the Applications Folder, which is accessible to all users, because it is in the ROOT directory, not just the users that installed them.  You can create an Applications Folder in a User's Folder and keep them for just that user, but it usually is the first way I mentioned. That way when you make a new user on the fly, you don't have to install all those apps again, waisting space. Also, that way you don't lose apps that may have taken time to install that other users need and use.

Applications that are installed to a computer through the App Store are linked to an Apple ID that was used to Purchase/Download it.  This is similar to iOS devices as well.  If I download an app on another persons iPhone using my account, they need my account to update it.

So this means one of two things:

Either your wife bought iPhoto (Or which ever other App is in question) or when you bought the computer, registered iPhoto to her account.

When you buy a new mac, it comes with iLife, and iLife is now downloaded through the App Store.  It will link those 3 Apps, to the Apple ID of your choosing so that if anything happens and you need to do a restore or something, you can download those apps you got for free again, no problem.

I had to do this when I bought my mid 2011 Mac Mini. 

So she either purchased it or registered it to her account, and that is why it is still on the computer, because it is an App that can be accessed by any user that is on the machine, so it wouldn't have been deleted when she installed it/registered it.  You will need her sign in and password in order to update it.

I hope that this information helps you out.