Quote - Solution is to set a Constrained Group of a couple of vertices around her neck, to force the neck of the cape to turn with her neck and make the whole cape twist.

Without being able to try it for myself right now, I'd concur with pjz99's advice to constrain around the neck hole of the cape; otherwise it won't know to turn with the figure. It doesn't have any constrained vertices set up by default. The other option would be to turn the cape manually before simulating, so the front is facing in the right direction.