My broodies hatch in the main coop, normally keep them in the main coop a couple of days after hatch, and bring them back into the main coop to spend the night. After the first couple of days inside they pretty much spend all day outside.
When I consider my main coop too crowded I sometimes putt he broody and her chicks outside in the run in a small coop. After a couple of days locked in there I turn them loose with the flock. The broody takes them back to that outside coop at night. When the population goes down in the coop (I process some cockerels and sometimes pullets) I move them to the main coop.
I keep water and food at a level the chicks can reach it in the coop and in the run, but they also have a big grassy area where the broody keeps them all day. A problem in the coop is that chickens scratch a lot. Bedding gets thrown into the water. So I put down a large piece of cardboard (think refrigerator box) on top of the bedding and put water on top of that. I have to clean off that cardboard every day or two. The chickens do scratch a lot.
I put water in a small fairly shallow dog bowl and fill that with rocks for them to walk on. That way they don’t drown in their water.