Hi there!
I would not recommend you put the broody hen with the others. First of all, roosters can distract the hen quite easily by bothering and jumping in the nest box too, so that may be an issue and break the eggs. Secondly, roosters could kill the chicks, but they tend to be more docile compared to the hens, so he may protect her while she broods.
Unfortunately, the other hens are the biggest problem. Once chicks are born, they get very aggressive, almost jealous and may attack both the tired hen and her chicks, a rooster is handy in this situation but in the 'crossfire' the chicks may get trampled on.
It's a difficult situation moving the hen and chicks while they are hatching, what I suggest you do is isolate them in the pen with the hens away and wait until the chicks have hatched, then you can either move the hen and keep the chicks yourself or house them both together so she can rest and look after them. Moving eggs while they are hatching is dangerous for the chick, and the hen may flap about if you move her and crush the tired chicks. So, it's best to wait and move when they are all ready.