We decided to tackle this head on, neither my wife nor I like conflict but it had to be done, so we sent the dog outside & sat the cat down, we explained our position & how we felt disappointed in the cat not upholding it's part of the agreement, we did not lose our temper or raise our voices we feel we did very well. Once we had finished we awaited the cat's response, it licked it's paw, got down off the chair arm & walked out without saying anything, it them proceeded to remind us it was time for it's evening food.
Our cat has half got the rat catching thing. She catches them, carefully carries them in, then lets them free in the house, where one at least promptly escaped under the cooker. I believe she thinks we need hunting practice so she brings live ones in for us to practice on.
She does tend to eat (whole) the smaller rodents and pigeons