Ditto two points--train the kids first, and holler OW and break off contact with the pup. No eye contact especially.
We use that on our dogs and people are amazed that I can let them stick their hands in our dogs' mouths and there is no biting. It also makes it easier to inspect and brush their teeth if they know not to bite.
If a pup is biting a person and won't let go right away, depending on the dog, I sometimes put a bit of their upper muzzle over one of their teeth and push a little bit. This confuses them enough that they let go.
We are working on the no biting thing with the new rescued little paw, Squeakers the Chihuahua. Those little teeth are SHARP!