I let mine brood and raise the chicks in with the flock. At day 18 I set up a barricaid so that other hens don't try to lay in the nest and potentially crush the newly hatching chicks. I make sure there is food and water available inside the barricaid and that gives mama a safe place to hatch. Since you are not sure of the exact age, you might want to go ahead and do that. Once the chicks are hatched, dry, fluffy and crawling all over mom and she has lost that glassy eyed broody look, I sit around and wait for her to bring them out of the nest to the ground and keep an eye out for how the other hens treat her and the chicks. I currently have a very respectful flock but I have had hens who wanted to attack the babies so that is something to watch out for.
Some people have luck moving then broody and nest. I have never tried. They say to do it at night that it is more effective. Once the chicks are active, you want mama with them so let her out so she can protect them. You don't want the chicks squeezing out on their own. The only down side to putting her in the cage is if mama can eat and drink from the nest, she will do so. This also means that she,very likely, will not come off the nest to poop and then you have a poopy, messy, unsanitary nest. That is also something to consider.
