Which is why momma is hanging back at the cage...she doesn't want a repeat.
I would not integrate them immediately but let them be sectioned off in a pen together where they can see the flock.
If you have especially vigilant higher pecking order hens, you may even have to wait to integrate at 10 weeks or so.
Too aggressive, you may wish to remove that hen from the flock and integrate the lower order mother/chick, then reintroduce the bossy one after she's had a good time out (like a week). That might knock her down a peg in the pecking order...or make her try to take her position with renewed vigor.
Never be afraid to remove and dispose of any hen that is overly aggressive. There is just no need for it. Pecking order is normal, some hussle and tussle to keep it to be expected, but nobody should kill or maime. That is too far for my humble flock.
LofMc