We have two Macs in the family, one registered to me, the other to the wife. Whenever I tend to updating both machines, I have to call in the wife, to let her enter her AppStore password for the iLife apps (Numbers, Pages, etc). However, I have those apps as well, but the Mac AppStore does not let me use my account for this machine. Is there an easy way to change this, so that I can update the apps with my account?
There isn't an automated way to do that.
You would need to request a new redemption code from Apple for all of the apps. I've seen them grant that for businesses that can prove they purchased the Macs.
For used Macs, I've generally bought a gift card for the buyer or discounted the selling price to account for the lack of license for the built in apps.
I suppose you could ask for a "do-over" for that Mac to Apple Support if you can't put both accounts in a Family Sharing situation and use the AppleID you want to access "puchases" from another account.