I do NOT recommend moving the hen until after she has bonded with her new chicks. I rushed that last year and had a panicking broody stomping on her new chicks, it was bad.
The way I have success is take the earliest hatched chicks and put them with her at night (as soon as they are dry) and take away the fake eggs. Early In the morning I put any more hatched chicks with her. Then I give them about 4 hours to get acquainted and then move all of them to a new place. (This is very easy if you have a low cardboard tray or half a box that fits into her nest box. I put that in when she’s off the nest on day 19 then I can move the whole family at once.) Since she knows her chicks are under her she is unfazed by the move and as long as she is still laying down I can add any more late hatchers throughout the day.
I’ve added a picture of my hen in her box. This pasta box is really great for this. It has one low side so it’s not in her way and when I put the chicks in I turn the box around so the chicks can’t fall out.
I recommend leaving her and the chicks with the flock if it is a safe setup. I have a big flock so I move some broodies to mini coops just to limit the chaos in the main coop during chick season. I just change to shallow water dishes and make sure the obvious dangers are dealt with when the chicks are babies and things have gone very well and the chicks are part of the flock from Day 1.