The difference between treating a new chick for a rupture and this hen is bacterial load, a "clean" wound, and length of time the intestine is outside the body, and how much damage the intestine has. I am not familiar with this chick with the protruding intestine you speak of, but it's a safe...
That's the saddest thing. The description of her going away from the coop when the others were heading to the coop to roost tells us this chicken is already dying. It also appears that this hen was attacked and injuries are probably much worse than it appears.
I'm very big on fixing a chicken...