If you separate the chicks from mama, let them grow up, then add them, it will work, but you are missing all the advantage of raising chicks with a broody hen.
I leave my broody in the flock. I do check under her every 2-3 days to gather stray eggs, but other than that I leave her alone. She gets off the nest - goes out and terrorizes the layers, looking like a beach ball, growling. They give her space. I do have a lot of space in my set up.
Mine always hatch in the nest, and then take the babies to the floor of the coop. She will create a nest there. The first day, I do put a chick water up and a bit of feed.
With in a day or two, she will take them out to meet the flock. They give her respect, and what you will notice is she will be between the flock and the chicks. The chicks explore, but stick close to mama. They get more fresh air, more exercise and are much stronger chicks that chicks that are kept safe in too small of area. The will crawl under her for a warm up or a nap, or even snuggle down on top of her.
If a layer gets irritated by a chick and gives a peck, the chick will scream bloody murder, and the broody hen will come over and clean clocks. The flock adjusts to the chicks, but the chicks adjust to the flock. They learn chicken society.
I try and get a board up on the roosts around 2-3 weeks, because the urge to roost comes on the broody hen around 3-4 weeks. Mine have alway gotten the chicks up on the roost, with the flock at about that time period. Right in next to the rooster and the layers.
Now at this time, there will be a difference in different broods. Some will 'wake up' and it will be like they totally forgot they ever had chicks. And a lot of people will try and introduce them to the flock then, and it is a wreck. I did have an old darling that raised a lot of chicks for me, and she did keep them next to her for a lot longer - but she was the rarity. Most quit by 4 weeks.
So I would let her out with the flock ASAP. I have heard horror stories, but that is when someone (with good intentions, separated the broody hen from the flock). Then the broody comes in as a stranger, and has to fight for her own space in the flock. But if the flock knows the broody, she will protect the chicks and they will stick to her pretty tightly.
Within a few days, mine will have her chicks out free ranging, climbing over sticks, going up hills, digging in the dirt - learning to be chickens.
When she 'forgets' the chicks, well they are already part of the flock. They are completely accepted.
When I brood chicks myself, without a broody, I still get them down to the coop/run by 3-4 weeks. I have escapes and a saftey zone, but they are much healthier than in a too small brooder.
Mrs K