@MacPack:
Is she playing rough, pawing and mouthing, or seriously biting them (not in fun)?
How old is your basenji? If she is a puppy, she is treating them like littermates and that can get rough. I wonder about spraying bitter apple on your kids?
If she is an older dog, she needs some structure, and long walks to get her tired out and use some of that energy. Then have your kids give her small treats, so she equates them with good things. There are whole chapters written on getting a dog used to kids, and 4 & 6 tend to active, running about and doing things that trigger 'prey drive'.
Basenjis tend to favor some family members but not usually exclusively, like some breeds.
Yeah…definitely...ours favor whoever is still eating
Seriously, the OP needs to determine if the puppy is acting in aggression (probably not) or play (probably). It can be really hard to monitor that age with the puppy, but it has to be done. The kids run and squeal and pester, and the dog thinks that is *awesome! Both kids and dogs need to have firm rules about what is allowed with their interactions. I tell my five year old, no running (unless you want the puppy to jump on you), gentle touches only, and the puppy tries to mouth your hands, you stand up with hands straight up, and walk away. As long as I am there to redirect the puppy, this works pretty well.
Kids generally don't have the social standing in the family from the dogs eyes for the dog to bother listening to the kids...just as MacPac said, they are siblings, not authority figures. The adults have to be there to control the situation until the pup grows up enough to understand the rules.
A positive reinforcement puppy class that welcomes families would be ideal. Good luck, let us know how it goes!