With your animal menagerie, I'm surprised you have a rodent problem. Before I had deer fencing I had no rodent problems as I had a major overgrowth of catnip, very highly invasive, and an early grower. At that time the nip-patch was populated by an ADHD ocicat and a 24 pound Maine Coon. Considering their constantly nip impaired states, I suspect that if they saw a rabbit, their dialog would resemble a Cheech and Chong exchange: Wow, man kool a rabbit. Yeah, man, far out! Nevertheless their mere cat presence was sufficient to control rodent damage.
When it was garden planting time I pulled up many square yards of nip plants and threw them into the yard to be mulched by the law mower. I was too late with the mowing and before I knew it we had a cat block party highly reminiscent of 60's other weed driven block parties. Cats of all stripes and colors who were previously highly territorial mixed freely without any signs of hostility or aggressive feelines! Mowing the weeds only intensified the pursistent aromatic distribution and festivities.
Around here the rodent tomato bandits are the tree rats AKA squirrels! The solution is to grow many more tomatoes than you think you will want!

There's nothing wrong with thinking
Except that it's lonesome work
sevil regit