Why is my App Updates linked to my wife's AppleID? I can't change it
if she 'bought' them, even on 'your' machine, they are tied to her Apple ID. You would need to re-purchase under your own ID. 

App Store purchases are not tied to a machine, they are tied to an ID

… or set up Family Sharing, which would allow you both to download/use any app purchased under that share, without impinging on general privacy.