Shell's got lots of good advice. The biting, too, is a very classic issue to have with a puppy removed from its litter so young. Most pups will start learning bite inhibition from their littermates once they are old enough to start playing together, but she never got that chance. Combine that with how puppies explore their world with their mouths and, well. You get a bitey puppy. Be really consistent with play or cuddles - teeth on skin means the interaction ends. On walks, brainstorm ideas to keep her from nipping passer-bys. This might mean walking her on a shorter lead and a front-clip harness so you have better control. It may mean teaching her to happily wear a muzzle (the Muzzle Up! Project website has great advice on this). Muzzling sounds scarier than it is, and with her being a pit mix it may be the best way to make walks safe for everyone, especially given her breed. Not because pits are inherently dangerous, of course, but because people may react much more strongly to being nipped by a pit mix than they would, say, a golden retriever.
For the older kids, look into the Dog Decoder app. This has lots of really great illustrations that teach dog body language. You can go through it together, and help them (and maybe you, too) learn when your pup is saying she's scared and wants to be left alone. Lili Chin, the illustrator for the app, also has a lot of great body language charts you can find for free online. They'll still probably need supervision and reminders, but it might help them feel more empowered to know how to interact with her and understand how she's feeling.
Definitely make her a safe space, like the crate Shell mentioned. The couch isn't great because of course you might need to use it while she's under there. A pen may also work, depending on the space you have. The important thing is that when she's in there, nobody is trying to interact with her, stare at her, take her things, etc. She's never grabbed and pulled out of it, either - if you need to move her, she gets called to you in a happy voice and rewarded with treats or a game.
I'm a big fan of Patricia McConnell's booklets, and she does have one for fearful dogs called The Cautious Canine. They're really short, inexpensive reads and generally have great clear instructions and tips. But fear is a difficult issue, so you may reach a point where books and internet advice can't help you further. Start putting some savings aside if possible, and research behaviorists in your area who use reward-based, force-free training, with bonus points if they're certified by a reputable organization like CCPDT or APDT.