T.R.
There is a BIG difference between biting (aggression) and nipping (behavior, usually driven in part by the breeds characteristics & children's actions). So, before you think about whether or not you should or need to rehome a dog, more needs to be taken into consideration.
What is the age of your dog? If under the age of one, this is a behavior that comes with immaturity, & should be dealt with by proper training.
What is the breed of dog? Herding breeds (shepherds & collies) will naturally nip in order to put kids where they want them (treating the kids like a "flock" they need to keep in order). It is best to consult with someone who has experience with herding breeds if this is what the dog is doing.
What behavior are the kids engaging in? If they are loud, active, & raising their hands, or holding high-drive objects (toys, treats), that can naturally drive a dog to nip at their hands in a form of play. It can get out of hand, especially if there are objects the dog wants that the kids are holding & not giving. This behavior requires training both the dog & the kids, to eliminate the behavior, & prevent it from reemerging.
If, in contrast, the dog is assuming a guarding position, with head lowered, whale eye (showing the whites of the eye), growling or standing fur prior to "nipping", then that is a fear/protective behavior on the part of the dog that can become aggressive if not trained properly, and this may not be the right dog for your family.
The safety of your children is important, & I would never advise any family to keep a dog that was putting that in jeopardy. However, based on your post, it is not possible to say "give the dog away" or "a little training will take care of this".
If you have more information to offer, I'd be happy to give more concrete advice. Feel free to message me privately if you'd like as well. T.