In my experience, a lot depends upon the mama's position in the social order. If she's always been a lower ranked bird, she may try to defend her babies and not be successful. Although most broody mamas are a force to be reconned with, some of them just don't have what it takes. These, I would keep separated until the babies are a little bigger but that the flock can easily see. If you have a separate run off the same coop as everyone else, that would be perfect. Fence off a corner in the coop if you can and since they sleep on the floor, you don't need to provide perches or anything, just food and water.As far as separating chicks after they are born - momma does a great job of teaching the kids and integrating them into the flock so I haven't found a need to do that even though I initially thought I would have to. Each time the broodies have stepped up and protected their babies from any curious or aggressive chickens. I have found that brooding them separately is harder to introduce the chicks into the flock and it takes longer too. Letting the broody do it requires little to no intervention on my part and they get moved into the pecking order easier.
For example my Smokey's first clutch was 2 wellies and 1 AM. They were just a day old and I opened their side of the coop to let her take them out when she wanted to. The alpha roo, a White Leghorn, hopped inside the coop and looked like he was just looking around when he suddenly snatched up one of the chicks and flung it by the back of its neck to the ground. Thankfully it wasn't hurt. But my docile tiny Smokey flew into a rage and attacked the roo & all the pullets standing nearby. After that I knew that Smokey would not have a problem defending her babies.
I was worried that my silkie Topsy wouldn't be able to take care of her babies around all the others because the others are large fowl. But, nope, she's raised two clutches and is on her third right now. She's a great defender of them and teaches them how to avoid the pecking order squabbles.
The momma leaves the chicks usually (there are of course exceptions) around their 4th to 5th week and they are on their own after that. But they would have formed bonds with other chicks and will be able to keep themselves warm by then too.