I pretty much leave a new family alone for at least a week or two, if mom is present. Her biting could be just her inexperience of having little ones around, or she could be responding to the stress of having visitors. As long as she has food, and water and a clean litter box and is not actively openly and aggressively hurting her babies, you might try just leaving her be for awhile. The kittens will still be there in a week or so, and she will be calmer not having so many looky-loos around.
I know it is hard because newborn kitties are the cutest, but the best thing is to leave them be or only visit when absolutely necessary.