age range in the coop

That is hard to answer. I've had a broody raise chicks with the flock that weaned them at 3 weeks, so it is possible. But just because it is possible does not mean there is not a lot of risk involved. The younger they are, the more risk. You are dealing with living animals. About anything can happen. I am firmly convinced that you need a lot of space for it to work too.

You have two kinds of aggression to worry about. First is pure integration. Chickens can be territorial. They might (or might not) protect their territory from any strange chickens. If you house them side by side for a while but where they can't get to each other, they will usually accept that the other has a right to exist. That's the function a broody performs. She protects her chicks until the others get used to them.

Sometimes you have a hen that will just not accept the others and will actively seek them out to destroy them. It has been fairly rare with my flock but occasionally you get one, and it is usually a hen, that is a pure brute. It is not a mature rooster.

The other aggression is the pecking order stuff. More mature chickens will automatically outrank less mature chickens in the pecking order. If the less mature invades the private space of the more mature, they will peck them. It is their right and how they maintain their pecking order status. If the lower ranked one runs away, then all is usually well in the flock. But if one does not run away, it is a challenge to the other and it can get really nasty. If you space is tight and the younger cannot evade the older, then if can get really bad.

Sometimes you do have older chickens that will actively chase the younger even if it runs away. This does not happen all the time but it does happen. If they have enough space to get away they quickly learn to avoid the older chicks. That's why it looks like you have two totally separate flocks. The younger ones are protecting themselves by avoiding the older.

Can you merge them? It is possible but really risky. If you have to try, house them side by side for a week or more and give them as much space as you can when you do merge them. Also give them separate places to eat and drink and as many places as you can for them to get away from the others. Things to hide under or behind or extra perches.

A couple times I have had a hen brood her own, I allowed her to raise them as she saw fit around the rest of the flock.  When my old chickens would free range one hen disappeared and I thought something killed her but one day she came out of the marsh with a bunch of little chics behind her and brought them all to the coop.  I always had roosters as well.  I have never once had a problem but the chics always had a mother around.

I would not attempt to integrate 3 week old chicks with 4 month olds. The 3 week olds will not be able to defend themselves. I usually wait until they are at least 12 weeks old to attempt integration and even then there can be a lot of fighting but at least at 12 weeks, they have a fighting chance. (Chicks raised with broodies are a very different thing. They have a mom to defend them. The other birds know it. And even they can get into a lot of trouble when Broody mama is done with them.)