That really sucks. Can your mum feed the cat and puppy in separate areas?
I do and yet don't understand why some places don't allow pets. Yes, they can be messy and destructive, but someone who allows their pets to be that way will likely be messy and destructive on their own, and pets are no worse than kids most of the time anyway. Besides, pets are family members - they're not just something you get rid of when you move, like an old couch.