I have read before that you do this. I would like to try integrating them right away. I have a broody right now. Maybe I'll try it this time.My hens hatch their eggs right in the flock right in the coop. I do have narrow nesting boxes, so once the broody gets established, the layers lay else where. But they are not locked there, or away from the others. The broody hen does not take anything off of anyone else and is established farily high in the pecking order. Mine have always been willing to take my arm off at the elbo. Growl and puff up when approached.
I know when the chicks are suppose to hatch, and I put a nest outside the coop and lock the layers out of the coop for about 24 hours. Then I open the gate and let the layers free range. The broody hen will have left the nest, created a new nest on the floor in the coop, and have the chicks outside, usually staying in the run or close to the run for a few days.
Now the hormones are high those first days, making your broody aggressive towards any other chicken. She will thump any layer that gets too close. The chicks learn to stay away from the layers, and the broody hen stays between them and the layers. I really don't have any trouble with chicks in the flock.
Many people, separate the hen and chicks and then try and reintroduce them to the flock when the chicks are older, what happens is the broody hen has lost her pecking order, and must reestablish herself. Her hormones have started to drop, so she is not so defensive of the chicks, and the laying flock sees the whole groups as intruders. And older hens can be dangerous to undefended chicks.