I have chickens, various 12G shotguns, an air rifle and rats. I poison the rats away from the chickens, normally by filling in all the holes after popping some poison (wheat covered poison that smells like aniseed). I set up traps where the kids can’t get to and lose their fingers.
The best way is to get a “humane” trap whereby the rat goes into a cage that is baited and the exit door drops down when they get to the bait. You can then dispose of the rats as you see fit. Seems to work well and avoids any problems with being a poor shot / poisoning chickens / losing the kids fingers.