One of my pet peeves is people who interrupt my conversion with another person as if I wasn't there without an "excuse me" or an apology. The same applies when speaking in a group and someone speaks over me as if I wasn't there.
Just curious how you will handle the situation if you do shoot the dogs. Of course if you shoot just one, the other may run away, never to return again. Keep us posted of any new developments.
If you go to court just have your neighbor prove the half-cat was their's. Did they take a picture of the cadaver and compare it with any photos of their pets?