Depending on how many chickens are in that space, it sounds like it probably is big enough to have a broody and her chicks in with the flock. Great!No way I could touch anything arm length. The coop is probably 3 times my wing span if not more and the run area is more like a small yard fenced in and covered with wire.
In that case, you can probably just use the dog crate to make the other hens stay out of her nest until after the chicks have hatched, and then let the hen integrate them into the flock.