Broodies take up to 3 days to "come out of their broody trance". The three days is great, as this allows the newly hatched chicks to get their land legs - so they can follow momma around when she finally leaves the nest. Takes a good 2 days or so for the chicks to rest from hatching also - it is a very tiring job, hatching.
Give her a small dish of crumbles within reach of her on the nest and in another corner give her a small dish with water (a couple rocks so the chicks will not drown). She will start to call the chicks to eat and drink right away.
She puffs up and pecks at the chick because her chick does not belong out of the box with you - it confuses her as all her chicks should still be tucked under her.
Does she have an easy in/out of the nest box? Will the babies be able to follow her easily? If not, once the eggs have hatched, move her and the babies into a small plastic dog kennel. This will allow you much more freedom with the bunch. I take the dog kennel out in the morning (mom/chicks in kennel), put them in the broody/chick area and let them out. I leave the kennel there, and put them back into the kennel at night - then into the coop.