My understanding is you have the hen and her two 2-week-old chicks in the coop (roughly 5 feet x 9 feet) running loose while the two 6-week-old chicks of unknown sex are in a brooder in the coop. You have an unknown number of hens, maybe or maybe not with a rooster, in some unknown-size run that are not allowed in the coop. I’m guessing the run is fairly decent sized? The rest of the flock does not free range but are locked in a run. The hen and her chicks and the flock can see each other through a small grill. The two 6 week old chicks are pretty much unable to see any of the others or be seen by them. I don’t know where the rest of the flock roosts at night. I’m assuming you want to integrate the new chicks with your main flock.
The first thing I’d do is take down that grill and let the hen and her chicks mingle with the flock before she weans the chicks and leaves them on their own. I don’t know how that will go so you’ll need to observe. I let my hens hatch with the flock and raise their chicks with the flock. My other hens hardly ever threaten a chick. If they do the broody hen promptly kicks butt and takes care of that. The rooster may or may not help the broody hen take care of his kids but as a minimum I’ve never had a mature rooster threaten chicks at all. Immature cockerels seem to be the biggest threat and my broody hens seem to take great pleasure straightening them out. I also have lots of room outside so the broody hen has plenty of room to work with.
I don’t know how much you isolated your broody while she hatched or how isolated she really is now through that grill. She may or may not have integration issues while getting back with the flock. That’s the main reason you need to observe closely for a while. The more you isolate the more “iffy” re-integration becomes.
At six weeks and in summer, your other chicks do not need any heat. I’d build a wire pen in the coop or somewhere predator proof so they can see and be seen by the rest of the flock. I don’t know how much the rest of the flock will see them in a pen in the coop. Let the rest of the flock get used to them for at least a week. Two weeks is probably better. Then open the door and let them mingle with the flock. To me this is more risky than the broody and her chicks. They won’t have anyone to protect them as they set up housekeeping with the rest of the flock. The flock has a hierarchy known as the pecking order and these chicks will be at the very bottom. I don’t know how big your run is or what other facilities you have to work with.
When you integrate you have different things to contend with. First is basic integration. Some, not all but some, chickens will attack strangers. This is where housing them so they can be seen really helps. They at least recognize the others as members of the flock. That is a big issue.
The other part is the pecking order. Each chicken within the flock has a certain social position. The higher ranked chickens have certain privileges. Once that is set up the flock normally becomes quite peaceful, but setting the pecking order up can get violent. Immature chickens rank lower than mature chickens. Some hens go out of their way to bully the younger ones. Some of them sometimes, again not always. What normally happens is that the hen will attack an immature chicken that invades her private space. The weaker chicken runs away. There may be some chasing involved but as long as the weaker runs away it’s no big deal. The younger ones quickly learn to form a sub-flock and just avoid those bullying hens. It’s possible you can have a hen that is a pure brute, one that goes out of her way to seek and destroy any weaker chicken. These are fairly rare but with living animals anything is possible. As long as the weaker chickens have enough room to avoid the older hens this normally works out pretty well.
One potential problem is that I don’t know how much room the younger ones will have to avoid the older ones. If they don’t have enough room to get away when they run away or to avoid the older ones to start with it can get pretty rough. The broody hen will take care of any integration issues with her chicks, but once she weans them and leaves them on their own with the flock, they are going to have the same pecking order issues. This is not about so many square feet per chicken. It’s about having enough room to run away and avoid.
If instead of wanting to integrate the entire flock you are talking about letting the broody and her chicks share the coop with the two six week olds, you may have real problems. The broody will protect her chicks from threats. She will probably see those two older chicks as threats if they are too close to her chicks. If the older chicks have enough room to run away they will quickly learn to avoid the broody and her chicks, but I’m not sure your 5 square meter coop is big enough for them to have room to avoid, let alone get away.
There are a few tricks you can use to stretch your space. Set up different feeding and watering stations so the weaker don’t have to challenge the stronger to just get a drink of water or a bite to eat. Giving them places to hide behind or under can help them avoid. Roosts high enough that the adults cannot peck their feet gives them a place to avoid. If you can fix a door to a pen so the younger ones can get through it but the adults cannot, they have a safe haven when attacked.
A lot of us go through integration with broody hens or with brooder-raised chicks all the time. My wire-sided brooder is in the coop. The chicks are raised with the flock and I have lots of room, inside and outside. I don’t have any problems when I open the brooder door at 5 weeks and let them mingle. If your chicks are not raised with the flock or if your room is tighter, you can have serious integration issues. I don’t know how this will work out for you. Your situation is different from mine. I wish you luck.