Isolating a broody and her just-hatched chicks where the rest of the flock can see them isn’t a bad thing. It gives the chicks a better chance to get mobile and to learn to eat and drink without interference from the other adults, plus it gives the hen and her chicks a better chance to bond and the hen a chance to teach them to obey her. I generally don’t do it that way, just let the hen bring the chicks off the nest whenever she is ready an let her handle everything with no interference from me, but it’s still a reasonable thing to do. But I want her to still be in full broody protective mode when the chicks are introduced to the flock. If she hatched where the flock can see her and has been isolated with the chicks where the flock can see her, she probably will have no reintegration issues herself. If she is some mysterious hen they’ve forgotten about that suddenly shows up with a bunch of chicks, she might or might not have her own reintegration issues.
A good rooster protects all members of his flock. Some roosters are better than others, but normally if the new chicks are introduced to him at a fairly young age, he assumes they are his. Sometimes a dominant rooster will help a broody hen take care of her chicks, especially if there is some problem. Helping does not always happen, but I have never had a dominant rooster threaten any young chick. Most of my hens don’t threaten a young chick either unless that chick wanders into their personal space, though occasionally some will. That’s when Mama kicks butt.
A story I like to tell and I’ve seen this many times. I’ve seen a two week old chick leave Mama’s protection and go stand next to the other adult hens at the feeder. Sometimes the other hens ignore that chick, at least for a while, but it usually doesn’t take long for one of the hens to peck that chick to remind it that it is bad chicken etiquette for that chick to eat with its betters. After that peck the chick goes running back to Mama as fast as it can run, peeping and with its little wings flapping. Mama ignores all this. That chick needs to learn. But if the hen that pecked the chick starts to follow it (usually they don’t but it has happened) Mama gets all upset and whips butt. You might be able to discipline my chick but you sure can’t threaten it.
There are lots of different ways to do any of this. They all have their benefits but also their potential drawbacks. Our individual experiences will guide us in what we do. With practically anything to do with chickens, there is hardly ever one way that is right for each of us where every other way is wrong. There are a lot of different things that can work with their own benefits and drawbacks. You’ll develop your own methods and style as you go. Welcome to the adventure of broody hens. It can be a fun ride.