It may take up to a week of putting them in there at night. They will see the older birds walk up and mimic, shouldn't take that long for them to get the hang of it. Big thing is to close the other coop door and not allow them access to it.
Of course they are ready to not sleep with momma. As they should be integrated with the flock I'd close off the small coop making the chicks can stay with the flock, go into their coop, so you don't have integration issues in the future. That's the beauty of broodies, they integrate the chicks...