Yorkie, you should go to the police ASAP. Puppies can nip, but this sounds like more than a nip. And in any case, the dog should not have been out in public, off a lead, where it could even nip someone, let alone actually bite.
Yes, the owners say they are trying to train it, but the dog should not have been out loose.
Even if all the police do is 'have a word' with the owners, it may be enough to stop it happening again, or worse.
I hope your DD is alright and hope that this doesn't give her a phobia of dogs.
Let us know what happens, and do go to the police ASAP.