I moved mine a couple of days before the eggs arrived. Glad I did because she wasn't happy. I wound up moving the nest box she liked with her, and that solved the problem. Do it after dark, in the evening.
Last year I let one hatch an egg in the coop with the others. I marked the eggs to be set so I could take out others laid in there. It worked, but you do have that problem of other hens jumping in the nest that the broody is using. I was out there every hour or two to make sure things were where they were supposed to be. So this year she is separated. I open the cage every morning, and she gets up and eats, etc., then goes back. (There is food and water in there but I don't see any sign she eats or drinks the rest of the time.) Good broody. I will open the cage and leave it open as soon as all the chicks are hatched. Mama protected her chick from the others just fine last year, and these are the same hens, so not worried about that.