Most of my broody girls stay with the flock.
I have covered cat litter boxes, cardboard boxes and plastic trays that they can nest in. Mostly that is just for the Cochins and Silkies but I also have a Welsummer that is broody on eggs right now in the flock pen. I just make sure that I mark the eggs that are set for brooding so I can take out the others when the girls may lay new ones in the same nest.
I feed my flocks that have chicks in with them the starter as well. I leave down oyster shell so the girls can still have that and I sometimes leave layer mash in the hoppers that are hanging up so the chicks don't get into too much of it. It won't hurt the flocks to feed starter for a while. I have some girls that are several years old that are constantly getting into my grow out pens and eating starter.
I have separated some girls into a rabbit hutch or small movable pen and it is fine that way, too. The hard part is integrating the hen back into the flock later. Sometimes they just can't get back into that good pecking order. And when mine raise the chicks with the flocks it takes off the pressure to find somewhere for them to grow up in another pen or adjust to a new flock.
I now move my broodies out if I want them to set particular eggs. I use dog crates or cages. Something so the hen can at least get up and stretch and the hatchings can't get out. I provide small food and water containers (I have those cups that hook to cage doors).
I have left broodies in with the flock and in the nest box, but other hens will keep adding eggs to the clutch. Other hens will break the eggs or kick them out of the nest. I lost most all my chicks that hatched in a nest box from falling out of the box, or from getting out in the yard and lost/drowned/snatched, or from crossing into another broody's clutch and killed.
My best integration was when I brought the dog crate into the chicken yard and surrounded it with it's own temporary yard made of hardware cloth. The hen and chicks could be seen by the rest of the flock. When the chicks were probably around a month old I started opening the gate and letting everyone run together. The mother kept using the crate for a couple of weeks then she went back to roosting. I moved their crate inside the coop and took down the hardware cloth. The chicks stayed in the crate at night for a while, then I built extra steps to the roost and they started to go up on their own. It was time consuming for me to manage, but it worked out well. Good mama was a Buff Orpington. I don't have hens raising any hatchlings this year.