E.B.
My dd was bit by a dog a couple of years ago. There was no ex or custody involved, but here's what happened.
The dogs did not have tags or collars, but they busted through their own fence so we knew who they belonged to. We called Animal Control who has a protocol in place for things like this. They instantly responded, with the police. The owner could not produce any records, but "thought" his dogs had gotten some vaccinations several years previously.
So Animal Control impounded the dogs. With rabies, if a dog is to develop any symptoms, it takes about 2 weeks. So they keep the dog for 2 weeks and closely monitor it. The owner is responsible for fees and board and food. After 2 weeks neither animal appeared sick, so my dd did not have to have shots. However, the owner could not pay the fees and did not get the dogs back. And he was barred from owning or registering a dog for a certain period of time.
We were told in the ER that rabies is a muscle disease and is usually transferred to a person when the rabies enters the muscle through a deep enough cut. Dd also passed that test because her bite was a flesh wound but did not tear the muscle. That doesn't rule it out 100% but it does somewhat lessen the possibility.
So I would definitely contact Animal Control in the city where the bite happened, and the police as well. Leaving a child with a dog like that is dangerous. Animal Control can give you some guidance.