We segregate Mommas, but let them back in with the flock once the chicks are eating and running around. Never had any problems, but we also free-range and have a good rooster. That may not work for you in a closed coop and run system, I've never used an entirely closed coop and run.
We segregate broodies because they will steal eggs. They will take eggs from other chickens. Sometimes bolder chickens will chase them out of the nest and lay new eggs on top of the nest--and the fight can damage the eggs. Far better to move momma, in my opinion.
I move the nest beforehand, into a small rubber feed pan. My nest boxes allow me to move this pan into and out of the box without too much trouble. At night, I take it, hen and all, and slip the rubber pan into a cardboard box. There are airholes in the side, and feed and water at one end. She should not be able to see much, but should be able to make out food, water, and the nest.
I transport the (closed) box to my preferred nesting location and leave it there, still closed, for several days, except when cleaning up the poops and replenishing food and water. I open the box when I'm confident she's bonded with the nesting site.
This has always worked for me, but my hens tend to be pretty determined broodies (usually the hens I have to move are bantam game hens.) On the other hand, if she's disturbed enough to break broodiness during the move, I'm not sure I'd trust her to raise a nest anyway.
While the chicks are growing, you can switch to all-flock crumbles and feed free-choice, if you don't already. Just supplement calcium on the side for the laying hens.
And do have a plan for roosters, of course.
