Yeah man I don't want to shoot it at all, and I'm actually skeptical about doing anything because my neighbor on the other side of me had there car window busted out by a rock because she asked the same neighbor to help pay for vet bills when one of their other dogs attacked her dog inside of their garage. But if I don't do something my wife and daughter take the risk going out to play.We've had multiple boxers and I've been around countless others. I've never met a 'mean' one. Without seeing it, he may just be doing his job (protecting his territory and letting you know who rules it) or he might be a problem. If he's come onto YOUR property, yep, that's a problem. We've got the same issue with two American Bulldogs. The difference is animal control has been called and come out multiple times. Nothing has changed despite the owner getting some heavy citations. It took a great twist a while back when the owners son was involved in a shooting in a drug deal gone bad. "Bad" dogs generally have bad owners. Neighborhoods are awesome....
All of that was probably completely useless except to say... I feel your pain. I haven't yet brought myself to take lethal action and I sincerely hope I never regret it.
Edit, just read your last post. Call the Sherriff's office if animal control won't respond and ask them what you are supposed to do.