I agree with pfrog. They really don't deserve to keep this puppy. Report them again.The authorities aren't clueless. The can assess how the dog is being treated by its behaviour.

It is wrong to steal a dog. But it would be very tempting to "relocate" the animal if the authorities are unable to change the family's behaviour. Maybe next time the dog finds its way to your place, wait until they come looking before you hand him back. If they can't keep the dog secured the dog could be run over.