Often multiple broodies work well together to hatch and raise chicks. Often broodies will imprint on their own chicks and chicks imprint on a certain broody so multiple broodies can raise their own chicks in the same general area and ignore each other, especially if they have enough room to stay separate. As always, I think room has a lot to do with chicken behaviors.
But I have seen broody hens fight over eggs just as they were hatching and destroy some of the eggs. Broody hens sometimes fight over the chicks, wanting to take them all over. Something I’ve never seen myself but others on here I trust have posted is that a broody hen might try to kill another broody hen’s chicks.
While it is possible the hens and chicks would be OK if you put them together in that pen, I personally would not risk it. I just don’t see any benefit in it, especially if they pen is not huge so the broodies can keep their chicks well apart.
Tinakevin, I see that you are in New Hampshire. Thanks for posting that so I don’t have to ask. It helps with this answer. You don’t know how chicks will behave at four weeks or any other age when you try to integrate them. I once had a two week old chick with a broody hen kill its hatchmate. No integration involved, it just decided to kill its hatchmate. You cannot predict how chickens will behave. That’s the nature of living animals. Some people like to say with absolute certainty that things will happen one way and only one way. I’m not one of those. We can often tell you what will normally happen but I’ve seen too many exceptions to what I recommend to ever give any guarantees.
I don’t know what your weather will be like in the next week or so. I don’t know what the coop and pen look like where you want to put them. At four weeks old chicks that have been raised outside with a broody should be able to stand pretty cold temperatures, they have acclimated. If they can get out of the wind and weather when they want to they will probably do OK. But thinking where you are and the time of year, I’d be a lot more comfortable at five weeks. So if you can stand it, I’d suggest you wait another week.
You could let the broody hens wean their chicks before you try to integrate the chicks. That could be this week, it could be another month and a half or more. I would not do that. When I decided to put the five chicks together, I’d put them all together at the same time. You have three different groups that probably do not know each other. They will have to work out a pecking order so have them do that at the same time. You could possible try to house them side by side for a week before you let them together but I would not. I’d put them all together at the same time when I could watch to see how they behave, probably a weekend for you. Be prepared to intervene and isolate a chick if it gets bloody, but otherwise let them work it out.
I would not worry about stressing a hen by taking her chicks away from her. Chickens by nature are prey animals. Broody hens do have a very strong attachment to their chicks, but they quickly get over it if they lose their chicks and get back to the business of laying more eggs and maybe hatching some more. Other prey animals behave much the same way. If they lose their young they get over it pretty quickly. It’s a survival of the species adaption. It does not have any bad long-term effects, they will not have any long term emotional effects. If possible, try to house the chicks where the broody hens cannot see them for a couple of days. That should make the break cleaner.
Since they are not used to being together, I’m not sure what the chicks sleeping arrangements will be. They may huddle together the first night, they may not. I’d check on them as it is getting dark to see where they are sleeping and move them to where you want them to sleep. You might need to do this for several nights until they finally get the message.
This is all just my opinion. Others obviously have different opinions and experiences.
My personal preference would have been to give all the hatching eggs to one hen and break the others from being broody at the start. Or if I did wind up with chicks hatching at the same time I’d give all the chicks to one hen to raise and break the others. That way you avoid all this uncertainty and drama. I’m not criticizing you, there are plenty of other people that do exactly what you did and just deal with it in their own ways. We are all unique.
Good luck!