I would leave them with the mama, and I'd leave them in the coop. Leave the door to the pet carrier open so she can take them out when she's ready. So far this year, I have had one broody hatch in the main coop, no separation at all after the babies hatched. She had them out in the run by the time they were 24 hours old. She kept them away from the other chickens at first, but within a couple of days, that little family was out scratching and pecking with the rest of the flock, no problem.
The second broody I let hatch is a younger bird, so I was thinking maybe not as high up on the pecking order, so I separated her and the chicks for a few days before integrating them. They hatched on Tuesday, I kept their part of the coop closed off until yesterday. When I opened it up, she ventured to the other side of the coop, but didn't go outside. Today they were outside with the rest of the flock, even near one of the older birds without getting scolded.
My third broody is in the main part of the coop so she'll be integrated as soon as the chicks hatch. I really do like that plan. The first year I tried it, the hen was killed by a raccoon when the chicks were about 5 weeks old. Not a problem! They were already accepted into the flock, so they had no problems.
