Lara has some excellent points & suggestion. I only want to say that dogs & puppies recognize children as "human puppies." As such, they are not naturally attentive to their authority when it comes to respecting space. Dogs can easily view children as competition for the beta positions. Since your puppy is still new to your household, it's understandable that she makes these mistakes.
It's not impossible or difficult to change this... it just helps to recognize this factor in the training system. Try out the NILFF Program (Nothing in life is for free) & it might help your dog to understand that the children have authority. Another method is to have a child go through puppy obedience school alongside the dog.
Oh, if she nips, even in play, say no or tell the child say no & ignore her for a while. If you/they have to, leave the room. Don't play tug of war games or anything dealing with the hands, arms, or legs. No wrestling. Rough play does encourage mouthing. It's natural for a puppy. Do keep your eyes on the situation....especially for the 6 year old.
Hope these suggestions along with Lara's helps you out a bit. Good luck.
toodles