I GOT HER!
I went outside to get the black stool and she was on the right side of the run.
I used the string to pull the door open a little, then I swung really wide on the right and got her to come around to the front of the run. I waited for her to notice that the door was open, and as soon as she wandered inside I shut the door behind her.
She was totally soaked, muddy and freezing, so I brought her in, got her cleaned up and blew her dry. She was very hungry, so I gave her some scrambled egg, feed and water. She's now in the brooder with her baby. Baby is very happy to see her! Hiding in her feathers and eating with her and everything. She hasn't acknowledged the baby super much yet, but she attacks my hand when I come near now, so I think that's a good sign. I think she'll need the rest of the day to recover, but a very happy ending overall.
Now back to my original plumbing problem.