Penny needs structured training. You don't have to spend 700 on a puppy trainer, but a puppy class is a must. What she's doing is asserting dominance over your children--she considers them as siblings and in a litter, puppies establish rank amongst themselves through dominance and submission. Young children also have high voices which sound like their own puppy siblings.
If she's resisting your "no bites" and getting riled up more, she's trying to assert dominance over you too. She seems to have a strong character, so you've got to get her under control before she gets too big. Penny can sense your children's fear and will only grow more confident because of it, so it's up to you, the adult, to be the uncontested Alpha here.
At ten weeks, she's still small enough for you to grab her by the scruff when she bites, give a firm shake, then put her on her side. Say "NO" in a deep voice as you do this--you can even growl, it's how momma corrects-- and hold her on the floor, one hand on her neck, the other on her body. She will squirm and struggle. What's important is that you do not let her up until she totally relaxes--this is a sign of submission.
I'm not for rewarding a biting dog who lets go. My concern is that she may be associating biting people with a reward. Biting is serious, so for me it's absolutely forbidden and no treats in sight if I have to correct her, just kind but strong discipline.
Not all puppy classes are equal. I would call and explain your problem before enrolling her. Your 6 year-old, athough pretty young, can be taught how to put her through her paces but until the kids are old enought to really show Penny they're not her siblings and are to be respected, you need to protect them.
If it's any comfort, Jazz was like Penny at 10 weeks. He bled all three of my kids and I nearly shipped his hindquarters back to the breeder. But learning about dog behavior (2 great books IMO are by the monks of New Skeet: How to be your Dog's Best Friend
and The Art of Raising a Puppy
) and getting structured training changed everything.
At nearly 7, he's the dog of my life and a true marshmallow. Has never even shown his teeth since puppyhood. Actually, he did: when Skye arrived as a puppy last year, to her only, and only until he got used to her. He was educating her, and it was between them.
All the best to you and Penny. You can do it.