It would be nice if a breeder or two would pop in here, I'm not, though I have had hens that felt comfortable enough at this tree house to go into nesting mode, but haven't had one enjoy sitting in their water dish.
Have you talked to your vet about this yet?
Since she is not hand tame, if you need to get her out of the cage, you can do so with little stress to her & minimal damage to you.....you'll need a flashlight, a travel cage, box or something to hold her/travel with her in, and a helper.
When you're ready, be at the cage & know exactly where she is, turn off the light (all light - completely dark), use the flashlight to make sure of her position (only an on then off), open the cage door & grab her around the neck & as you do, talk softly to her.
When you grab her, you need use your thumb & forefinger, with the thumb under her beak so you can control her head & beak, with a bit of upward pressure...your other three fingers need to wrap her body as best you can. If you're not sure of catching her this way, you can use a tea/cup towel, but if you're not right on your catch, she'll probably start moving around the cage. Also, if you have to use a towel, you need to be sure you have control of her head or get ready for the bites. If you have small hands, enlist the help of someone with larger hands.
Good luck
Since you have other birds, it might be wise to practice the catch on one you handle regularly.....