I would talk to the law there, but pretty sure the owner of the dogs not on a leash is the responsible for the bill. get your facts from the law first, and then talk to both owners about the bill. the dogs have to be on a leash. they can not run free for exactly that reason. If they don't pay for the bill then file a compliant with the police department and get your money back that way. but if both of them pay one third of the bill, because there can be a leash law for cats to, so your mom is responsible for one third too for the cat not being on a leash.