What you need to do, Mick, is wall off an entire small room with a thick, bullet-proof armour glass wall, and make that the "rodent room". In it will be housed several hamsters, rats, and gerbils, running around happily on their exercise wheels while your cat Esmeralda watches in total frustration from her side of the glass wall. Entrance to the room will only be achievable through a double set of security doors in a small antechamber with a cat-annihilating electrical beam set to go off if Esmeralda gets past the first door.

This should do it. Your daughter will experience the joy of having rodents in the house, and your cat will be forced to put up with it.

I should think this could be done with a modest expenditure of funds, as long as you put aside purchasing any more musical instruments for, oh, maybe five or ten years.

It's worth doing! Get to it.