Have you checked to see what the HOAs rules on dogs might be? Mine would never permit a dog to be unleashed FOR ANY REASON. Perhaps they could do something.
Ok I posted too soon. Should have read further. My apologies.
We had a dog in our neighborhood that was on a leash but that was too big for the owner to control. It got away from the owner and grabbed a terrier like the dog from Frasier. It crushed that dogs chest and it died. This was like a Tuesday. On the weekend, it got loose again and attacked a man who was walking. The dog picked the wrong time. Another person was also walking at the time and he was armed with a small 22. Thus ended the terror dog. My point, I do not have firearms in my house but after the first attack I began the process to get one. In a suburban development with an HOA.
An out of control dog that attacks an animal for fun will attack a child one day. I see no distinction nor will you convince me otherwise. I would not let that dog roam free out of respect for my fellow human beings.