If I were you, I'd seek the advice of legal counsel. If what you say is, in fact, true, you are not in the wrong here, but you are OUTNUMBERED (mayor - likely extends to the police, board, neighbor with cousin on the board). If the law is on your side, make it work for YOU. That means you...
Go back to the original post and title of the thread: "Neighbor is threatening me and my chickens". Threats, slander, and abuse shouldn't be tolerated by anyone. It's called fighting back and defending oneself. How is that a "wrong"??
Some folks will just take abuse; others will stand up...
You can play the game too. I'm sure there's something that they do that you don't prefer; make it an issue and stick your nose in their business. Maybe their grass doesn't smell the right way, or their dog does whatever (barks, craps, stinks). If they bother you or engage you, file a...