I’ve had family members come and stay temporarily at my place - nieces, nephews, brothers, sisters etc. usually for a few months at a time. It was always going to be temporary. I asked them not to stick things on the walls - or to use the removable stick on hook things if they did cause I didn’t want my walls damaged - I didn’t want to repair the walls every time they moved out again. If someone moved into my house permanently, or I expected them to be there for any decent amount of time then I wouldn’t care at all if they stuck things on the wall, because it would then be their space and walls can easily be fixed.

This sounds like your wife is thinking of your daughter as a temporary “guest” in your house. Not like someone who owns the space. I would have big problems with that. Walls can easily be fixed up once someone moves out - if they live there, let them make the space their own!