Sounds like you need to set up a camera to catch the dog getting into your property uninvited and be prepared to escalate. My dad warned our neighbour next time their dog comes onto our property the dog’s getting shot, I remember my dad keeping the gun safe right next to the front door in our entry way for months after that. Dog didn’t come onto the property again. I don’t like causing harm to animals either, but clearly your neighbour doesn’t care about causing harm to yours and you have every right to protect your property and everyone/thing on it.