We successfully moved a hen on a nest this weekend but fortunately she was in a plastic box and we did not move it too far, about 30 feet. She tried going back to the old location but we guided her to the new location where she she found her nest box with her feathers and eggs inside. She has been off the nest and back on again so she seems willing to settle for the new location.
We once moved a tractor coop over a nesting hen to keep her safe by lifting it up over her. We have a hen on a nest now that we put a shelter over to hide her from the crows better. It can work to move a nest but moving things around the nest can work too if the nest is not easily moved.