Hi, welcome to the forum! Glad you joined!
I'm not there watching them so I can't be sure what is going on. I usually give chicks at night so they have time to imprint on each other but I have successfully added chicks in the daytime. Not only do the hens have to accept the chicks the chicks need to accept the hen. I've had failures, but not many.
Yours should be young enough so they have not imprinted on something else. You say yours are running around, eating and drinking. Mine can't do that the way my nests are built. With my nests they are pretty much forced to stay with her. I don't know if that has an effect or not.
Your hen pecks at them when they get close. What does that look like? Is she pecking them hard hard, trying to kill them or run them away? Is she pecking them more for discipline, telling them to do as they are told and get under her where it is warm and safe? Or maybe from curiosity, what is this thing. Chickens use their beaks to explore the world. I don't know if that hen is a threat to them or not.
I let my hens hatch with the flock and raise the chicks with the flock from Day 1 but I have a relatively large ground-level coop. It sounds like you may have a small elevated coop. A broody generally needs some room to work with to take care of and protect her chicks. I don't know how well she can protect them if she decides she wants to. I've never had a broody hen fail to protect her chicks from other adults, but some people I trust on this forum say they have. You do not get guarantees with living animals, even if the circumstances seem identical. You never know what any of them might do.
It's been a while since you posted. What did you do and how did it work out?