At least where I live, Animal Control Officers are considered "cops" and go through the same training as the others, initially, and wear the same uniform. But I don't know about other areas... Where I live, if an officer is aggressively approached by a loose dog, it will be shot, especially if...
You mention that they are also harassing your other neighbors. In a way, that is a good thing, especially if you and none of them have ever been complained about before. Hopefully they are all level headed types who won't go off the deep end and do something criminal in the face of all the...
Maybe get one of those video door bells, that will automatically record audio/video whenever someone comes to the door... Text or email when you can, when you communicate with authorities involved, and don't delete any of it. Don't forget to take pictures of the yard if complaints are...