M.L.
Just as human babies put everything in their mouths, puppies do, too. It's part of their baby nature. Unhappily, puppies have little puppy teeth. Ouch!
AND... this little gal doesn't know what's proper playing and what isn't. When she goes after your hands or feet, it's because they're moving, or because they're there, and she thinks, "Go for it!" After all, that's what she did with her siblings back at Mama's house.
You need to protect the puppy and your daughter from one another for a while. I always use baby gates with puppies. I keep the pup with me in the room where I'm doing something. There are several reasons, one being that if she isn't in the room with me doing something approved, she'll be in another room doing something unapproved. (Another is because I take a puppy outside after every meal, every nap, and once every hour that she's up. The fewer mistakes she makes in the house, the faster she'll learn what to do when she needs to go.)
Provide your puppy with a lot of things she CAN chew on. I don't advise old shoes because she can't tell what's old and what's new. But give her squeaky toys, puppy nylabones (not food bones that can splinter), and clean cloths soaked in water and frozen. When she starts nibbling on something she shouldn't, say, "No," or "Don't," and give her something she can have. When she starts pouncing on toes, give her something approved. It is well to keep shoes on during these few weeks. By the way, this is something perhaps your daughter can help with - you don't say how old she is, but she can hand her puppy a squeaky toy.
I'm sure your four-footed girl is trying the best she can. But she's just a baby and it takes time for her to learn. If you can work patiently with her and keep your sense of humor, she will be smart and confident later on - not afraid of you but looking up to you as her leader.