I agree that a little over a week is pretty old to try this. Some broody hens will adopt about any chick, even this age or older, but some won’t. The normal thing is that the chicks and hen talk to each other before the eggs hatch so imprinting has already started. The older the chicks the more the risk. I agree to put them in under the hen after dark. One of three things will happen the next morning: 1) She adopts them, they accept her authority, and things are great, 2) She ignores them. Doesn’t hurt them but doesn’t nurture them either, or 3) She kills them. No one can tell you which of these she will do, you need to be there at daylight to watch what is going on. Another possible scenario is that she wants to adopt them but they don’t accept her authority so she disciplines them by pecking to establish her authority. This is not the same as her trying to kill them but sometimes it is not easy to tell the difference.
I’ve never tried introducing chicks this old to a broody, they’ve always been straight out of the incubator. And when I’ve tried this, my broody hens have always been broody at least two weeks. Some people on here say they had no problems with hens that have been broody just a few days but the rejection rate seems to be higher with hens that have just gone broody from posts on this forum. I suspect that is because some hens go into full broody mode from the start, while others only go into it partially. The hormones that cause the hen to go broody are acting up but have not hit a full 100%. The hen cannot count the number of days she has been broody but the hormones have to have fully kicked in. If she has just gone broody this does not guarantee failure, it just adds a little more risk.
That second coop sounds like a good place to try this. Leave them isolated in there until they have bonded, the hen is finding them food and keeping them warm. This should only take a couple of days, long enough for you to be sure she is caring for them. Then you can let them roam with the flock. Some people like to do this with a new broody for a couple of days so the chicks become mobile and get used to eating and drinking without interference from the flock, but yours are already over a week old. They are already mobile and eating.
There is a real good chance the broody will take them back to this coop at night instead of taking them into the main coop, but I don’t know for sure she will do this.
Good luck!