I agree with whats been state above, and I can't not express fervently enough that dominance training is NOT what should be used with a Basenji. This is a old school tactic that has lead to very aggressive dogs & biting habits. This form of dominance behavior with these type of dogs could endanger your children, as your dog doesn't know it's place or how to communicate with you properly out of fear of physical retribution.
Niping and biting are all apart of how your puppy experiences the world, dogs don't have hands so they sense and feel with their mouths. How was your bite inhibition training ? That should have started the moment the pup was brought home. When teething bites are too hard a high pitched "yelp" should be emitted and play time / all stimulation must end abruptly. This is what puppies do to each other within their litters, this is "dog" language. Your kids should practice this as well, it is only with consistency from all family members that your puppy will begin to change it's habits.
Also remember all dogs are not the same, just like people, so what worked for your other Basenji may not fit your puppy. I would grab "Other End of the Leash" by Patricia B McConnell for clues on working with your dog and not against it. Posture, eye contact, reactions, those all matter here. "The Puppy Primer" by her prob couldn't hurt either.
As all B parents say, a tired Basenji is a good Basenji. So more exercise for this dog is more than likely required. An hour outside is scraping the bare minimum, so if you can increase the walk times do. If not, try giving your puppy complicated tasks inside, kibble and peanut butter in a Kong toy (freeze it if your pup gets it out too fast) can entertain for a while, a good pizzle stick sometimes hours - Basenjis crave mental stimulation so games or puzzles (hiding food in objects for them to get out or agility training) are very helpful tools here.
Finally search the forums thoroughly for topics you have problems with because so many of us have experienced the same things, there are golden nuggets of advice all over the forum from many experienced breeders and owners who are extremely family and Basenji savvy.
Good luck