Help? Broody Jail in Laundry Basket

Hi, long-time lurker here. I have two young laying Americana hens, no rooster. One has gone broody - it's probably been seven to 10 days but hit hard in the past three to four.

Over the past days, she has stopped laying but is constantly brooding in the nest area. She's eating. I have been removing her and putting her in the yard on "chicken recess" and have included some extra treat food with the regular food. She is pooping okay and has no mites or bothersome areas, afaik.

Big issue: She has pulled her feathers and now has a naked underside. And we think she may have lost weight.

Today, I have removed her to a bathroom near my computer area -- I WFH -- so she is basically right beside me. We've modified jail in a laundry basket until a dog crate can be obtained. She is in a very cool space as opposed to outdoors in the heat (today's high 90 and very humid). I have the fan turned on her and the A/C is on 77. She is on the floor with some cardboard under the basket.

Leaving the other hen alone is the main problem - they are a bonded pair, if that is a chicken thing. I plan to take this broody hen out for recess this evening, so she keeps that part of her routine. I would like to let her sleep in her coop but understand this confinement could take three+ days.

Any encouragement, tips or tricks are welcome. Questions: 1. Should I get a dog crate? 2. How do you deal with poops when a chicken is inside? I'm picking up and flushing. 3. When will I know she is broken of this phase? 4. Do I need to worry about the "sister" hen? I am visiting her every couple of hours. 5. Should I dunk this girl in water?

All to say: I turned into a crazy chicken lady within about six weeks, and here we are not even at month three.

Thank you!