I do not see where the chick is being traumatized, can you point that out?
Pecking order can be brutal and an isolated chick often struggles to fit back in with the group.
If she is not being picked on or injured, then the chick should stay with her flockmates.
I agree, a better photo of the pink thing would be good.
I would separate her. Chicks picking at that can cause damage.
Hard to tell if it's prolapse or intestine, but either way it needs to be kept moist if there is a protrusion. Honey, vaseline, coconut oil, anti-inflammatory cream, etc...