Dealing with a broody hen

I have searched about trying to find some info on this. Unfortunately I have been unsuccessful. My problem isn't that she is broody, that's wonderful! It is the obsessive brooding and where she has decided to sit that is troubling me.

I have another banny hen that is also brooding. We call her mother hen because she reminds us of the hens from the Bugs Bunny cartoons, and she has tried to hatch out eggs as soon as she started laying. She will be a good mama.

But my White queen has tucked herself under a detached dog house roof, next to the coop. We had placed it there to help them get out of the sun during the summer. But now it is fall, the nights are in the 30'sF {-1c} and I can not see her staying warm. Mother hen is in the barn near the nursery where there is a heat lamp. Mother hen will also leave the nest to eat and drink, while the White Queen does not.

I thought about moving the white queen. But if I do that, will she lose interest in setting?

The best course of action that I can think of is heading off to the co-op today and buying some mash. I can heat up some milk and feed it to her warm. That will make sure she is staying warm at night. I usually don't do this until winter, as I can't keep the heat lamp on {light determines how chickens lay, too much light will burn out the layers} If only I knew that she was indeed the one eating what I leave in there for her.

Mother hen belongs in a different harem than the White queen. White Queen and her consort are the same silkie breed, he has no other concubines. Mother hen belongs to the Golden Buffs harem. The Golden Buff is a stud! He is also a bantam, and his harem consists of only one other banny {Mother Hen} then he has 3 adult Ameraucanas {full sized} The standard rooster isn't thrilled with this set up, but the hens are happy to be in a non abusive relationship. I wonder which rooster will win the hearts of all those new coming of age hens we have out there. Probably the Golden Buff as he doesn't pull at their tail feathers like the standard does. Oh these are the days of our coop.