You an do either, but if you choose to leave them with the flock, I would make sure that you're available for the first three days or so, and can keep a good eye on them. It sounds like your flock has never had a broody and chicks in it before, and they might not react well. Usually they do, but not always. Also, you want to make sure that the broody's doing well with the chicks. Sometimes, they're great setters and terrible mothers.
Seems sort of cruel to let momma do all the work of hatching out the chicks, but then not let her have the babies, but you can do it. I only separate mum and babies if she's a bad mother.
Get the chicks down once they hatch. No sense disturbing the nest site. Also, chicks have no idea how to use ramps, either, so if you have one leading into your coop, you might need to set up separate accommodations, or just physically go out and bring them in when it's dark or raining.