What would you sue for, they paid the Vet bill, right? Usual out come in court would have been to pay the Vet bill, that is what people sue for. They paid the bill, what would you sue for? I think your best route would to contact Animal Control & explain what happened. This has happened twice but there is no record with Animal Control that it even happened, you could have proved it has happened for the second time but there is no investigation if there is no complaint. Call or go to Animal Control & learn what your rights are. Maybe they can order the owners not to allow the little kid to take the dog out any more. They own a very dangerous dog, maybe they can order the dog be muzzled every time they take it out.
If you is no complaint/report there is no investigation. Start now so something can be done before this happens again.