I would draw up a letter and send it registered mail, tell the dogs owner that if he doesn't stop the dog from entering your property you intend to dispatch it. It is your legal right to protect your property from predators, unfortunately in this case is is a dog.
The letter opposed to "telling" him will protect you from him saying something dumb, as people often do, like "he said he was gonna shoot anything that came over there" or "he said he was going to get a gun and now I am scared". Once the letter is confirmed as picked up, shoot the dog.
A client called me a few months ago, said coyotes were driving his cows through the fences and hired me to deal with them. I set up and when the animals emerged in my scope it turned out they were a beautiful pair of German Shepard puppies. I tracked them down to the next door neighbour, a guy renting a country house and told him that I was hired to stop his dogs from crossing the fence and that if he did not find a way to prevent them from coming over the next time he sees my truck it will be to hand him the carcases for disposal, or I would dispose of the bodies or a fee.
They took the proper steps and kept the dogs at home. I don't know if I would have shot them, they were beautiful! I may have tried to catch them first. Either way, it ended.
Every province has its own laws dealing with pets running wildlife, the OP had best take care to finsd the right answer for his province, then I am sure he will take the appropriate measures...
