What you are describing has to be done in two operations. For its not a logical one step operation. Also how you describe intersect is not how intersect works. Your want to do to two thongs so just do them.
One) add the rectangle wind up with the union on the circle and the rectangle an the disjointed star.
Two) delete the star you wind up with your keyhole
The intersect of your A and B is:
Paths have and addition mode that selections do not have and that is exclude which delete overlapping area.
There is no join overlapping selection AND delete none overlapping selection mode.
The 4 Selection mode are New, Add, Subtract and Intersect
The 5 Path modes are New, Add, Subtract, Intersect and Exclude