I agree with this. Animals will sometimes wander off to die. I think that’s what your hen was trying to do when she went away from the coop instead of going in to roost. At this point, I think the kindest thing you could do for her is to end her suffering.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 bet the chick probably wasn't free ranging amongst an adult flock that may have injured the wound, further contaminating it and worsening it.
You can't just stick her intestine back inside and glue the wound shut. She would be dead from infection within 24 hours.
Here's what it would take to fix this hen, and a vet clinic would need to do it. Fully irrigating and cleansing the abdominal cavity of bacteria, isolating and repairing any tears in the intestine. Closing the wound enough to keep the intestines inside but not so completely that bacterial laden fluids can't drain. IV antibiotics and nutrients to stabilize the hen and coax her body to fight the infection. Most vets would advise euthanasia, but some might be happy to charge you hundreds of dollars to try to treat her and ultimately euthanizing her.