The town we are moving to this summer recently lost their trained police dog because someone saw it running towards their chickens, assumed it was a coyote and shot it dead. Personally, I would be a little angry to learn that a very expensive trained dog was killed because of someone's fear of losing their livestock - note that no birds were actually killed, it was just running towards them. I would have hoped that someone would approach the dog first and shoo them off before shooting. This was a different situation entirely than what you're going through though. It seems clear that these people don't care about the welfare of their animals or anyone else's. Such a shame, and such a terrible example for their kids. Ugh. How about trying to live trap them first? I'd trap them and drop them off at a shelter somewhere 100miles away. I doubt they would care or notice that their dogs had gone missing. I agree though that they should be reported to the sheriff because anyone with such a neglectful attitude towards their pets is probably not doing the best job of feeding & caring for their kids. It never hurts to get families like this on the radar as it were. It also doesn't hurt to have an established case against them because shooting pets, however feral they might be, could be really misinterpreted, especially on the internet. You really don't need some crazy social media campaign calling for your heads with people across the globe getting angry at you without knowing the whole story. What a crappy thing to have happen in general though, sorry you are going through this. Yuck.
PS I bought our Bouvier a bright orange vest to wear, not that she's trained for hunting, but I'm terrified someone will think she's a bear and shoot her on sight. I'm used to walking her off-leash up here but don't know that I can do that once we move to Texas no matter how well-trained she is.