Foxhounds?

Just build a decent coop from the start to keep chicken safe at night, and let the foxes roam freely the planet eating as much mice, voles and rats as they can catch. They love that job.

Ms yellowkitty will develop quick the sense to keep away from its path, or show their nails, or climb a tree.

Dry ice is frozen CO2. Rat nests usually have two holes, an entrance and an exit. Close one, place dry ice in the other and close the other hole to seal it. The dry ice melts and floods the chambers with CO2, no more rats.

It's considered more humane and safe than poison. Some cities use this method.