I don't think mine would ever use a bucket for a nest. You will need to add some fake eggs to whatever you set up for her to lay in.
The reason she wants to lay so desperately in the coop is because she feels it's safe for her future offspring. Hens like to lay where others are laying.
It...
Unfortunately that happens sometimes in a flock. Seems instincts tell chickens to go after any odd acting or unwell birds. It's a survival instinct to drive them out or remove them permanently.
Having a smaller set up will often make things worse. How big is your set up? If there's not enough...