Another angle, if you can't get her to go to bed in the coop (or, until you do...) is to see what you can do to predatorproof the tree.
If its branches are interwoven with other trees', or if they hang low over a fence or other "stepstool", you may not be able to do much -- but if it is a more or less isolated tree, such taht the only way up for a fourfooted predator is to climb the trunk, you can get some 2'-wide metal flashing from the hardware store (or improvise with similar material). Wrap it all the way around the trunk, about 4-5' off the ground if possible (high enough that nothing can jump up to get a hold beyond it). Poprivet the ends together, making sure you are creating as flat and ungrippable a seam as humanly possible. Then screw it into the tree at a couple of places along the top. So now you have a (hopefully) smooth and ungrippable sleeve around the tree, a little way up. This won't help vs owls of course, but can really reduce the chances of a raccoon or similar critter coming up for a chicken dinner.
Good luck,
Pat