Luna Petunia!
Some hens do seem to get poorly during molt.
A little buttermilk with white cooked rice will help with the loose stools, plus the buttermilk is a good probiotic. Mine love it!
Plenty of water for sure and see how it goes.
Offer her some mash free choice, plain water and a little rice with egg. Continue with the coconut oil.
I would let her eat and see what happens.
Is she pooping?
You can give the coconut oil anytime no worries. I would give her 1tsp twice a day.
Treat for Sour Crop and deworm. Is the crop pendulous at all?
https://www.backyardchickens.com/articles/how-to-treat-sour-crop-and-impacted-crop-and-how-to-know-which-one-youre-dealing-with.73607/...