Its is a difficult one, isn't it? If she likes it in the coop, could you perhaps let her roost in there with the others overnight, and then seperate her in the morning? If she still seems to have a good quality of life, ie is bright and not obviously in pain, could you perhaps divide your run with netting or mesh, so she could be in her own section and could see the others with no risk that she would get pecked? Then she would have some company through the wire and if it ever became possible, would probably be able to rejoin them with no social problems or further pecking. The others may be pecking her because she has been out of the run for too long and they have formed a social order without her, so they see her as an intruder to be repulsed.
If you can keep the prolapse clean and do your best to keep it in, she may have a chance, but you need to face the fact that her present state may only be a temporary respite and a complete cure is unlikely, especially if she tries to lay again and strains to do so. She is at risk of peritonitis, where an egg either travels the wrong way down into her gut instead of her oviduct, which can happen in hens, or breaks inside her if it has a soft shell which she strains to expel, and either of these happenings will cause bacterial infection and a lot of pain. So if she becomes quiet and hunched up and stops pecking around, that will be the time for the hard decision maybe.