If you read enough posts on here you'll see we do this all kinds of different ways. Some people like to isolate a broody and her chicks for various lengths of time. Some long enough that they have to handle integration themselves instead of letting the hen handle integration for them.
I prefer to do it like small farmers worldwide have been doing it for thousands of years. I let my broody hens raise them with the flock from when she brings them off of the nest. I don't isolate them first. I'm not saying my way is the best way or the only way. We all have different circumstances and sometimes what works for one does not work for someone else. I think if room is tight other ways might be better. Mine have over 3,000 square feet outside to work with. It's not true free ranging but close enough for me. And my 8' x 12' coop has room.
My hens hatch in a nest in the coop. When a hen starts to hatch I put food and water on the coop floor so the chicks can get to it when she brings them off of the nest. She normally keeps them in the coop for a couple of days, then takes them outside to the grass. After that she takes them out all day every day and brings them back into the coop to sleep at night. I don't have any nests on the coop floor they can get in, she takes care of them on the coop floor. Wherever she decides to squat down they sleep under her.
I've never had a problem with a broody failing to keep her chicks safe from other adults. The rooster has never been a problem, he sees them as his babies and either ignores them or helps Mama take care of them. Usually it is ignore. On rare occasions another hen may threaten her babies but a mad Mama hen handles that quite well, whether she is normally at the top or bottom of the pecking order. The others seldom bother the chicks anyway but it can happen. Some people do have issues with this, but I never have. I think letting her hatch with the flock so she is not a stranger and having a lot of room helps.
If your hen has been sleeping in that kennel there is a real good chance she'll return there with them to sleep at night. it is a good idea to check on them as it gets dark to see that they are inside an safe. I have had a couple of chicks get separated where they could not get to the broody, they trapped themselves. if that happens they will be giving a loud peep, you'll know. I'm down there at dark anyway to close the pop door for the night so it's not an imposition for me.
I think that raising chicks in the environment they will live in right from the start gives them a stronger immune system. I feed dirt from the main run starting the second day in the brooder to get hem started.
I make sure there is food and water where the chicks can get to it and check on the whole flock when I lock them up at night, not just the chicks. Other than that I leave everything up to the broody. She does all the work.
Good luck.