We do something similar. We nailed a cage to the side of some rabbit hutches in an area of the run protected from the weather. This keeps hens with their new babies until the chicks are big enough to be on their own.Yes, he definitely did, for once XD
The problem is,
the coop has tons of roosting space, and 6 boxes, but isn't very big (5x6ft).
The run however, is fairly big (20x16ft or so). So I can't section off a part of the coop, not without making it much smaller and harder for the hens to navigate.
I DO have a small dog cage, maybe 2x4ft but it would only fit in the run,
plus I could stick it underneath the metal roofed part of the run for shelter.
Only thing is the bars are a bit wide, I'd need to do something to it near the bottom to make sure the chick wouldn't be able to squeeze through.
Would something like that work? I don't love the idea of the chick and broody being stuck in a cage outside the coop, but if it's the only option, eh...
The cage is off the ground so it stays dry and coccidia don't run rampant. If the weather were drier, I would let mom and babies out of the cage sooner, but it's been really rainy here. I lost a couple of chicks that I let out of the cage too soon, along their mothers.