I can't imagine how frustrating this whole situation has been for you. And while it's easy for us, a bunch of strangers on the internet, to play Monday-morning quarterback, it's not going to change what has already happened.
That being said: not2cleverred's comment about hiring an attorney to write a "cease and desist" letter is the closest thing you have to a legal option. And as Red mentioned, it might just inflame things. Because there's not a negative consequence if they don't cease. Or desist.
So your options are: 1) ignore them, 2) negotiate a "cease fire" or 3) put your Christian faith to work and love on them. Pray for them, treat them kindly, and tell them, honestly and sincerely, that you're very sorry that their dog died. Because although the poor dog annoyed you with his barking/digging, I'm sure they loved him. Be the kind of neighbor that you'd imagine that Jesus would be. Because there's no law that you can invoke that's going to make them nice.