She really needs to come inside to be bathed and dried thoroughly before putting her back out in the coop. If you could just bathe her vent area, that would be good. Chickens with this kind of problem usually require a few days of soaks to get the skin to heal. But this cannot be done if they are out in the cold. If possible, bring her in, treat her, dry her, then take her back to the coop.
She could have suffered a partial prolapse, or part of he cloaca could have been exposed as she was laying an egg, which in turn, caused the others to peck at the red. Or she might have vent gleet, a fungal infection of her digestive tract. The runny droppings could also be from a reproductive disorder or infection, and the vent pecking can damage the vent where droppings slowly constantly drip out. That drainage can cause burning of the skin, and in warm weather, attract maggots.
Vent pecking can easily lead to cannibalism in chickens. Some reasons are overcrowding, not getting outside to roam around, boredom, a lack of protein and a balanced chicken feed in the diet, and some breeds can be more aggressive than others.
What do you feed? How much room is there for the chickens?