wow, can I ever feel your pain!
we have idiots living next door to us (really, you can't believe how not smart some people are). long story short, since they moved here 7 yrs ago, they've had a rotweiller, 2 pit bulls, a pb mix . .. . .see the recurring theme?? NOTE: It's not the breed, but the owners who are responsible for these dogs having bad reputations.
We put up a fence to keep their menacing dogs out of our yard. I'd try to walk my dog on a leash, and their rotti would run into our driveway to menace our dog (drooling, stare down, etc) until we'd go back into our house. I'd phone them and they were just like 'oh, sorry, it won't happen again' but it always did.
their house is notorious for those dogs. runners and walkers have altered their routes, school bus stops have been changed so kids wouldn't have to stand/pass there etc. lots of complaining, but nothing on paper.
one day, my teenagers are leaving for school. my border collie runs into the garage w/ them, (door was open) and their pit bull was there. chewed her up, requiring stitches, pain meds etc. At that point I had had it.
Called animal control, who spoke w/ them. Promised a fence, this will never happen again etc. 2 wks later, no fence and their dog was seen wandering the roads. I filed a 'dangerous dog' complaint and took them to court.
The judge took one look at that dog muzzled, w/ a pronged collar pulling the owner around and saw my problem. He agreed and now, if that dog is ever, even for a second, seen unleashed/unfenced, one call to animal control gets him picked up and euthanized, no questions asked.
2 days later they put up a fence and I've never had another problem. No, they didn't pay my vet bills (they told the judge they would).
I have a dog who's skittish and I think could be a fear biter. We've done lots of training etc. to build her confidence, desensitize her etc. to no avail. She's sweet w/ us, but not trustworthy w/ others. When people come over, she's confined. If, by some freakish circumstance, she were to bite someone, I'd have her euthanized.
Your neighbor, like mine, is being irresponsible. People like that, in my experience, won't do the right thing by themselves, unfortunately, so you just might have to see animal control. Good luck.
Valerie