When you really think about it. Trapping the dog could also save the dogs life and benefit the neighborhood. A free roaming dog is a menace to the neighborhood and the dog could get run over by a car. Trapping it would likely force the owner to either take better care of the dog or re-home it.
sometimes animal control will loan you the cage. I think you should trap that dog a few times and see how the neighbor likes the fines. Maybe they will get their own fence to keep their dog at home.You will still have to get your own fence or electric wire because sadly there will be other dogs.
Whether or not you shoot the dog, your chickens will still be dead and there will be another dog coming along sooner or later to kill your next flock unless you protect them (do something before they are killed).
Build a stronger fence. If it's not your uncle in laws dog, then it will be some other dog or whatever. If your chickens mean that much to you, give them a secure yard.