How secure are your run and coop? If you do not want to create an enemy maybe you can dog proof your run. I have mine enclosed in 1/2" hardware cloth and it withstood a two plus hour our attack by two labs who did everything they could to get into it. I have it on trail cam. I have never...
As many people on here say "A dog on its owner's property is a pet, a dog on my property is a predator."
I would first talk to your neighbor and tell them your concerns, hopefully they will take it from there. If not you could call animal control and file a complaint. If there is any way...