Might look at putting some windows and vents in the dog house.
Good point, I just noticed the dog house pic. A window with hardware cloth to the right of the door might do the trick, though with a house that size the older hen may want the whole thing to herself for now.
It also does not look predator proof and if it isn't then IMO it doesn't really matter where the pullet sleeps as long as she doesn't get caught outside in a storm.