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What???
I'm not talking about a painting on a wall, I'm talking about a living creature. If I'm worried that you might be doing something that could hurt it then yes, I have the right to ask you to stop and you should listen. Maybe I have to spell this out:
1. Both parties agree to move in together knowing full well two cats come into the bargain. The non-owner should expect reasonable mess incl. hair, kitty litter etc. The owner should be responsible for this.
2. Both parties are agreeing to share a space with the cats but ownership would ALWAYS rest fully with the original owner. She's paying the vet bills, feeding and cleaning (hopefully). This doesn't mean the other roomie doesn't have access to the cats or can't interact with them but she really should listen if the owner asks her to stop doing something with them that concerns her.
3. Same goes if the cats are doing something that annoys the roomie. Owner's responsibility, always.
If that makes me a dictator then Hitler was really something else.