The first step seems obvious, how in the world would your neighbors know you have an issue if for the past more than 10 years it hasnt been an issue ? They think that no-one cares about dogs running around on open property. Yes, let them know that you dont want dogs on your property and to please keep them off of it. These are peoples pets and no-one has ever raised an issue about them talk to your neighbors
Sounds like you may already have been killing their cats, or potentially. Any reason you are killing cats on sight ? I know they are not a predator for anything you are hunting, they are not canines, they are in the same niche as the wildcats, the bobcats, are you killing them too ? Both cats are keeping down the disease carrying rodent population. Same for foxes, why are you just killing all carnivores ? I was taught that we were supposed to eat what we kill, and otherwise to only kill what was a threat to lives or livelyhood
As far as your last question, even though you did ask, it would go against our forum rules to answer, I think....