I leave mine in the coop with everyone. I did this for 3 girls last year. I marked eggs and had to check and remove any new eggs laid each day. This worked out GREAT last year as the ones that were broody must have been a bit higher up (or my older girls aren't jerks)........
This year I have 1 broody.... Things went great for a couple days so I gave her some eggs, she was in a large shared box that only her and 2 other girls used (they all laid on one side of the shared box which was the side she was sitting in). One of those girls had no issues swapping over to the other side.... My older girl REFUSED to swap over and pecked at the broody until she left then that one sat on her eggs and laid her eggs..... Ok.... so I moved the broody over to the other side of the box and all seemed to be solved for a day or two. The one that beat her up went to the normal side of the box and laid her eggs no problem, the other one that was still laying laid her egg in the correct side so all was wonderful....... Then one of my other ones decided to go in and beat up the mom (not sure why as there wasn't really a reason and the one that did it isn't even laying even though she is almost 11 mo) then scratched around in the nest box and eggs were all over..... So I gathered the eggs (was missing 1 that I couldn't find anywhere) and put a cardboard box inside the nest box thinking that may help since she couldn't really fling them around and it put the sides a bit higher so not as much room to stand and scratch around. NOPE didn't help. today on day 8 (I had candled last night before I moved everyone in the shallow box) for some reason my broody switched sides of the nest box to sit on the fake eggs in the other side. So then the other girl went in poking around in her box, then was scratching around etc (I watched it back on my camera since I was at work), box got tipped over but think that was at the very end. The eggs ended up getting broken and eaten.

I think this broody just is NOT high enough on the dominance chain to really defend her nest/eggs/babies against the others. So now I am going to have to break her since it isn't working out.
So IF you want to leave her in the coop it can work out but I will say be sure she is dominant enough that the others don't bully her. I am not sure if that was the issue or if my 11 mo olds are just jerks and the ones last year weren't jerks???