How can i get rid of rats?

rats live under my dogs' houses and live on the dogs' leftovers. the dogs will catch one every once in a while but alas the rats are elusive not to mention prolific. i'm afraid to use poison for the obvious reason, dogs eat it too. snap traps are out, again, i don't want to hurt the dogs. the pesky rats refuse to go into the live traps i've bought, baited and placed around. now that they have a safe home, they venture out and feast on my garden and pick and choose flower plants in my landscaping. i haven't actually seen them in my garden but we have no rabbits. (the dogs ARE good for something). i saw something quick and grey scurry through the flowers and i'm blaming the rats because it's near where i've seen them. HELP!