You're having a rough time of it Kris, I do admire your determination to help these ladies any way you can
I agree with the other posters that she has a reproductive problem going on.
One thing I noted was that she is leaking fluid - is that coming straight from the vent or does it seem to be coming from the swelling - is that oozing fluid? (is the skin leaking)
I would say that she is suffering from Ascites which is a symptom of an underlying condition (I highly suspect a reproductive problem). Since she is not yours, then I'm not sure if her owners would allow you to drain her or if it would be better to leave her be. Draining is usually a temporary "fix" but might make her more comfortable since she is straining to poop. Likely swelling/fluid is pressing upon the intestines making it hard for them to function properly.
If you do decide to drain her the video is in the thread that
@coach723 pointed you to.
https://www.backyardchickens.com/threads/swollen-abdomen.1289236/#post-20901729 Draining can introduce bacteria/infection into the abdomen, so there is risk involved, if possible, antibiotics would be good, but I know those can be hard to come by.
I do see the point of view to go ahead and put them down too. A lot of times that is the best option. This is something you will have to consider - whether or not she is in good enough shape to try to give her more time or to humanely put her down. Each situation is a bit different. You are the one that's there and can evaluate her.
I'm very sorry that you are having to deal with all this. I know you care for these ladies. Whatever decision you make, it will be the right one.