I put up a wire pen inside the run for our purchased chicks. Used Mama Heating Pad for a broody. Worked out fantastic! The Bigs could see the Littles but couldn't hurt them. Then when they were about 3 and 4 weeks old (two different ages of chicks) we wired the door in such a way that they could get back in but the Bigs couldn't follow. Seamless integration. Chicks are now 5 weeks and 4 weeks old, no problems at all! You have a broody hen so you wouldn't need a heating pad.
For our broody we butted a dog crate, front door open, right in front of the nest. It had both a door on the front and one on the side for my access to fill water, etc. Kept it right out in the coop. You can do the same thing with some kind of enclosure built within your coop. If you bring mama in with her chicks, then you might face problems reintroducing them all to the others. So my vote is always to keep the Bigs, the Littles and the Mamas in the same area with as much visual contact as possible.
The x-pen we used for the babies out in the run. The "cave' you see is where they went for a quick warmup and a little security - also where they slept at night.
Agatha our broody, sitting on her nest. It was a large wire dog crate with two openings. Oh, and Daphne just had to snoop - again! I set up the broody pen before the chicks hatched, (actually chick - only got one out of 15 from the shipped eggs) and she was very content in there. She kept him in there for a few days before she started getting antsy and I propped open the side door full time. It worked very well.
