I have one of those humongous pine trees and they have a play area beneath it and when under there they are very hard to see because the branches droop down onto the ground. And mine are just like yours they do spend time out in the yard and it seems they know when it's safe but I think my goose tells them, I don't have a rooster.You could always consider planting bushes for them to hide under. I let my chickens free range for parts of the day in my 1/2 acre fenced in yard and they spend 85% under the four bushes I have, 10% under my large tree and the remaining 5% (if that) in the open. I have lots of hawks and eagles where I live so I was worried about getting them but they are no dummies. My rooster spotted a large bird (think it may have been a vulture but unsure) made his funny little warning noise and they were so tightly packed under the closest bush it was almost comical. Sorry your poor flock has been being terrorized by them. I hope you get something figured out for your hen and any future chickens you have