Our dog was attacked by neighbor dogs through the fence. Her surgeries have cost $7,000

Did their dog ever leave their lot?  If not, might be a tough case to win.  Their dog can be loose on thier lot.  If it got into your lot and attacked your dog, then I think you have a case.  Send them a letter with a demand.  If they don't pay, file with the magistrate.  Did they violate any local ordinance and were cited?  Just b/c the dogs fought doesn't mean you have a viable case against the neighbor.