I’ll assume you have 12 chicks just over a month old, not some a month old and some 4 days old. I’ve had a hen wean her chicks at three weeks, leaving them totally on their own. That’s pretty early but 4 weeks is not unusual at all. Unless you still have snow and ice on the ground them not sleeping under her should not be a problem.
I’ve also had chicks just a few days old sleep on top of Mama or laying close to her, not under her. Again it depends on your weather but even if they are just four days old it should not be a big problem. If they get cold they will force their way under her and another one will pop out.
I don’t know why you ever separated the hen from the flock, but many people do that. Then when you move the hen and chicks back to the flock, you have to do an integration. That’s why I like my hens to raise the chicks with the flock, integration is not a problem. Anyway you have a situation to deal with.
There are different things I can think of that might be going on. When a new hen is introduced to the flock, the rooster welcomes her back and established his dominance over her by mating with her. With your hen being broody, she may not want to be mated and is resisting him. Most broodies will. But that rooster has to be the dominant chicken so he has to mate with her to establish that dominance. Most of the time the broody will just run away, but with chicks she can’t do that, so she fights back. The rooster may be just trying to integrate her back into his flock.
Or it could be something totally different. A broody hen is very protective of her chicks. If the chicks are raised in the flock, the rooster is tremendously more likely to help Mama take care of the chicks than harm them. A good rooster takes care of all members of his flock. But since they were not raised with the flock, Mama may see the rooster as a threat to her chicks, so she may be trying to “protect” her chicks from the rooster, even if he poses no threat. The broody may just be confused as to whether he is a threat or not. He may just be trying to help her with the chicks.
It’s unlikely but it is also possible the rooster is trying to protect his flock from these strange new chickens. Roosters and even more common hens can be territorial and try to keep strangers away. So the hen may legitimately be protecting her chicks.
That’s all I can think of right now. Usually the more space you have the easier these things go. Mama just keeps the chicks off to the side and there are pretty much no problems. But when you integrate you can have problems. Good luck on this.