Oh, I almost forgot, we did have a similair experience about 20 years ago. My DH and I had 2 dogs, a shepherd/malamute cross, and a shepherd/lab cross. We raised them together, and had always let them out in the yard to play and do their thing, even though we had no fence. We thought they were staying right in the yard, as when we would look out or call them, they were right there. Wrong. One day, I let them out, and thought they were right in the yard the whole time, and brought them in a little later. Well, a couple days later, one of the neighbors told me that my dogs had been running the neighborhood that day---as on others---and had gone to another neighbors and killed their pet rabbit! This was so up setting for everyone. The rabbit had been this family's only pet, and they treated it better than most people treat their dog. Unfortunately, even though I went out and found the same type of bunny from a 4-H breeder, and brought it to their house, they were too upset about the loss of the other one to be ready to replace it. My dogs had killed the rabbit because the people had left it tied up in the back yard for a few minutes unsupervised---which wasn't wise, but still not their fault----my dogs were on their property. Anyway, I ended up keeping the bunny---DH had to build a cage, and the woman whose rabbit had been killed, actually came over to give me some supplies for my bunny-----I hope things can become as amicable between you and your neighbors.