First off, I had to laugh cuz your name is baddog and your dealin with bad dogs.
Anyway, I had the exact same thing happen to me. I didn't have time to post on IC about it though, soon as the dogs broke one board I went and hollered at the owner. Respectful but firm, look man, I got kids that be in my yard and I don't take no chances with my kids, your dogs breakin through the fence. I almost shot him but my family wasn't in no real danger at the time so I figured I come let you know so you could do something about it. Dude asked me what I suggest, I told him get some plywood and nail it up along the fence. I had like 2 pieces in my backyard I wasn't using so I used them on my side in the most dangerous spots. Dude didn't have any transportation so I offered to take him to home depot in my truck to get 4 more pieces, he nailed um up and the problem was solved.
Sometimes you gotta communicate man, 95% of altercations are from lack of communication.
I got a pitbull, its one of the nicest dogs I ever owned, big scary lookin thing but the nicest dog you'd ever meet.
If you really don't want to TALK to your neibors Id suggest going and getting some plywood (its pretty cheap) and lining your fence with it yourself. Don't let pride get in the way of your familys safety.
good advice