That certainly ups your ante, so to speak. A nip and a bite are two different creatures. First off - I will say your breeder shouldn't be selling goldfish, let alone puppies. An ethical breeder will take back any puppy at any time for any reason.
Yes, you can keep him and continue to work with him. While not a correction I would usually recommend - if grabbing him up by the scruff of his neck impresses him, do it! But if you use that as a correction for snapping at the children, continue to use excellent treats to reward correct behavior around the children.
If you decide to rehome him, please, please, please go through a reputable rescue group. You MUST tell everyone that this dog does not like children. He might make an excellent pet for an older woman that wants a companion and doesn't have children visiting.
Personally, I don't mess with dogs that bite children and had that bite broken the skin, there would have been a trip to the vet.