I do not think this is a
prolapse. When they prolapse, the inside of their vent actually sticks out of their body.. it looks like an internal organ.. you will know when you see it >.< The link posted above has good pictures of prolapse.
She is missing a ton of feathers on her butt and the skin looks very red and irritated. Are feathers missing from anywhere else on her body? It's good you separated her from the other chickens, she needs a quarantine time.
I don't know that it is necessarily vent gleet. Is the wetness in your photo from her bath, or is her butt wet all the time?
Actually, just saw that you said she was very poo covered, so it could be gleet. The treatment for gleet is rather simple, so you might as well treat her for it.
The
vent gleet link posted above is a great resource. Here is my condensed version:
- acidophilus capsules spread into dry feed *
- ORGANIC apple cider vinegar WITH the living mother* (organic is important): 1tsp per 1 gal water
- bath. you already did this, yay! you might have to keep bathing her depending on how it looks each day. make sure that she has a roost to sleep on where you are keeping her indoors. If she is forced to sleep on the flat ground, the poop butt problem will get worse. I recommend diluting epsom salt in the bathwater instead of soap or vinegar. Alternatively, I had the best luck creating a garlic brew by boiling/simmering water and 4-6 cloves for several hours.
- garlic douche using garlic brew - natural disinfectant
- 24hr fast followed by 24hr laxative diet (OACV water), then reintroduction of feed+acidophilus
* = appropriate for overall health of all chickens in your flock
Fresh gloves of garlic minced up and added to water dish is also a natural immunizer and protector against disease, adding to the overall health of your flock in general, or helping out a sick one. I feed garlic to my birds all the time. They get their choice of garlic+OACV water or regular clean water daily.
Aside from the vent gleet treatment, I just discovered a product called NuStock. It's made from pine oil, mineral oil and sulfur. "It has proven to be effective for fast relief of all types of skin problems. Nu-Stock also helps to eliminate certain types of growths on animals." This stuff is good for all farm animals and even pets!
You are supposed to apply it to the red irritated area, but do not bathe/rinse it off for 3 days. After 3 days, rinse it off, and if the area still looks red, you can choose to re-apply it. It helps the skin to regrow, and the old layer will come off after 3 days, leaving nice healed skin underneath. I've used it for abscesses, infected skin, vent gleet, and bleeding C/W's.
It's also good to cover up any little blood spots on combs/wattles to keep them from getting pecked, since nustock is yellow.

Good luck!
edit:
here is what my natural chicken keeping book says about
excessive moulting and
regrowing plumage:
Quote: