you need to build a trap for it. if you make the trap part of a not moveable structure like the house, chicken coop (if it can't move) or a tree for a corner, then trapping the dog makes it really easy to prove that it is hunting your animals on your property. legally you could get someone to shoot it for you, or at lest call pest control to get rid of it.
A dashcam is pretty cheap and would give footage of it approaching the coop and getting trapped, to prove that it is on your property, without your encouragement.
You can hide and say you can't do that to a dog, and it just means regret when it tears your pets to pieces.