You must be a very patient, kind neighbor. But the behavior of your neighbors is very disrespectful and you shouldn't have to put up with this.
Dog bites and dogs peeing & pooping on your property is not a right of dog owners. I would never let my dogs run on other people's property. I could see if the dog accidentally escaped and pooped on your lawn but I'd certainly clean it up myself!! You can try spraying vinegar in and around the perimeter and where he usually poops and pees, dogs hate the smell. Not sure what it would do to your landscaping though.
A dog that bites should, at the very LEAST, be muzzled! This should not be tolerated at all. Someone can get very seriously injured - then what? I would put my foot down on this one. Is the dog off leash? Does it charge at you? If so, keep something with you, (big stick), spray him with a hose, scare him off. There is no excuse for this dog owner. HE is responsible for the health of the dog, and if he knows the dog has bit before, HE needs to do something about it. You have every right to defend yourself, and children against getting bit.
I would talk to these people in a matter-of-fact way. Appeal to their sense of fairness (I mean really, this is not right) If they can't understand your concerns, then you have no choice in notifying the town, especially in regard to a biting dog.