We have two cats as well, but we have a retire racing greyhound. The cats have both tried to put the dog in her place, but the cats lose. They now just leave her alone, and she lies on the bed.
Being off today I was watching the dachshund chase the mean female around, she got slapped with the claws and yelped then went back for more. Its funny watching them. The male cat is mellow.
I let them keep their claws for defense, the puppy can be mean. Even though the leather couch corner looks to be sandblasted from claw sharpening.
get a cat that weighs even half the weight of the dog & the cat would eat the dog for breakfast...