Hi hello, I am a newbie on chicken hatching and brooding but just thought hop on the bandwagon. Though do take my advice with a pinch of salt.
I would say leave the eggs and chicks with the mother hen and avoid handling on days 19 and onwards if possible.
The reason for this is the more handling, the less likely the eggs are going to hatch due to disturbance.
The hen and chicks bond a couple days before hatching as chicks do chirp in the egg after they internally pip, and the hen often responds to their chicks to encourage them.
Along with this, the mother hen gives heat. Teaches the chicks what to eat and what not to eat. How to perch and roost instead of sleeping and pooping in the nest boxes. Overall I would say that the chicks don't make your ears bleed because it has it's mother.
When the first hatches, they don't need food for about 2 or 3 days so don't worry about feeding them. Until all the eggs that are able to have hatched, I would leave them unless they absolutely need food and water. Plus a chicks chirping helps it's siblings hatch too.
However moving the hen too much may discourage her from sitting on her eggs that still have yet to hatch.
I would agree that it would be wise to take the hen and chicks out of the main coop and run. And I would further suggest that you put them in a separate coop and run somewhat near the main coop, ensuring that they can see each other.
My reason for this is, for some reason a hen of ours has been out of the coop for about 2 weeks and when she was put back in with her previous coop. An all out brawl happened between her and the 3 other hens.
If you do plan on removing the hen and chicks completely, I would recommend slowly reintroducing them to each other.
Good luck and I hope some of this information helped a bit !