Power changes and trim forces. related to position of Center of Mass (CoG), or Center of Pressure?
Your intuition is correct.  Each of the three principle axes of the aircraft originate at the center of gravity.  Therefore, all rotation in either pitch, roll, or yaw occur around the CG.
The center of pressure is a place along the chord where the lifting force acts on the wing.  It is not a pivot point like the CG is.  In fact, an increase or decrease of lift will actually produce a pitching moment around the CG if they are not co-located along the longitudinal axis.  This contributes to the relative stability (or instability) of an aircraft.