Glad that your children are not toddlers and you have been very sensible in getting your pup when your children are older. The best thing about them being older is that they will listen to you and learn how to behave around a puppy much better than a younger child.
Pups do bite, scratch, drag, I'm glad that you realise that is normal puppy behaviour, trouble is children as already said are the main targets for play like this, even with the document supplied to adhere to (excellent piece) the best way to protect your children is for you and your wife to be the playmate, not your children.
My children helped to train my girl, they were the ones with the treats teaching puppy to sit, down, stay, roll over etc, enjoying our walks together etc, that was their roll, they had pup sleeping on them, greeted her, cuddled her fed her at times and that is all that they did, when pup was calm she was theirs with my supervision, when she wanted to play or started nipping I took over that roll and removed her from my children as pups hurt. If she was having a mad 5 minutes she was put over the dog gate with her toys and she could have an energy burst with my children safe.
Puppies grow up and of course your children love your girl, but you need to protect them both from each other, so talk to your children about the fact that the pup needs to be segregated from them at times to keep them safe and you need to take on the roll of playmate and keep her from nipping, scratching and pulling your children around, pups are little devils and children hurt easily, yes they are cute, but pups are far from the image of cuddly teddy bears, they can become 'family' dogs when older and your in control of them with STOP! and other commands to help a dog to live with it's humans.
You can control a pups behaviour by teaching it commands, but you can't stop it, it's natural, especially at this age, so just remove the pup from your children and take over the roll of playmate.