I understand how it is with trying to accomodate separate pens of broodies, mamas & chickies, growing chicks, and the rest of the flock. Makes the chicken chores go on forever each evening & morning. The wire cage should be effective, and it's fine to keep it in/near the regular coop. You can try to let her out after 2-3 days, see if she'll rush back to the nest boxes to brood or go hang out with everyone else.
I have lots of mixed-breed bantams who keep going broody. I had been putting them in turns in the Broody Buster, but recently I've been setting them with eggs from the full-sized flock. I have a friend who wants the pullets to start a laying flock, and I'll keep the cockerels for the table.