Heads up, I just looked at your photo again and think they need ventilation added to the coop. Unless there’s an open window not shown in the photo?
Well spotted! Also that coop looks pretty small for 6 large fowl chickens which means ventilation will be more of an issue. It only looks to be about 3x3 which is way too cramped if I am right. Also, I cannot see a door on it which is a concern for predators getting in maybe I am missing something. I appreciate that you have it in a cage but weasels/stoats/mink and rats could all easily get in through that size wire mesh by the look of things. I don't know if you have any of these predators in your area or other similar sized hungry beasties that like to order fresh chicken off the menu, but it is important to consider.
I'm not sure what is wrong with your girl. She may be trying to pass a soft shelled egg. That really takes it out of them.