Who is liable if our dog hurt neighbor B's dog that got into a fight on another neighbor A's property?

I believe it would be your father in law (whose dog was not on a leash) and the neighbor whose dog came after your dad's dog. I don't think they'd stand a chance trying to get your father in law to pay any vet bills as their dog crossed the road and came onto another property and also was no leashed. Basically, both are at fault.