I currently have two broody hens with chicks and 3 broody hens on "nests." I'm overrun.


All but one is a first time broody.
My first broody of the year is one of the lowest in pecking order and was very easily chased from her nest for about the first week and kept moving boxes, so I decided to put some eggs in the incubator just in case. Well none of her eggs ended up hatching but 8 hatched in the incubator. A couple days before they were due to hatch I moved her and her eggs into a large dog crate with food and water. The crate is in the coop so she's still with everyone else. I decided to give her 3 of the chicks. The other chicks were placed under a heat plate behind a fence they could go through but the big birds couldn't. So at night I took all her eggs and shoved the 3 chicks under her. She accepted them without any issues. The next night I opened the door to check the food and water and while doing so momma ran out. She ran around the coop like her normal cockoo self and even jumped on the roost ready to go to sleep. I put her back in the crate and she settled right down. On the morning of day 3 I opened the door and let them all out. She has been an attentive and protective mamma. She even pecked at one of the older ducks when in got too close. Even the flock queen, who is a bit of a butthead, would never dare to take on one of the ducks. She also adopted all of the other chicks over the course of a week so they are all one happy family now. I think the whole experience has been really good for her.
My second broody (second time broody) managed to hatch an egg in a upper level nest box. I must have counted my days wrong so I hadn't moved her yet. I moved her, the chick, and her remaining eggs to a different dog crate with food and water and shut them in. She stayed on the eggs for a couple more days until I took them. (It has proven very difficult to hatch at my altitude.) When I took the eggs I left the door open so momma and her chick are with the flock now.
So to answer your question in a more direct way... I let momma and chicks out with the flock after a couple days. I wanted to make sure the chicks were strong and agile enough to get away from the older birds. It helps that the majority of my flock is super mellow and they haven't shown any aggression towards any chicks.