You have one problem. The trouble code P0081 is telling you what is causing your problem. If the voltage the ECM gets is not correct, the intake VVT solenoid will not function correctly and will cause the intake timing on bank 2 to not be correct, thus rough running on bank 2. You won't get any engine timing codes because the crank angle sensor does not see anything wrong, your issue is specifically on bank 2 intake cam, more specifically the wiring for the solenoid that controls the intake cam on bank 2.
You have said you have proper voltage at the solenoid, what do you consider proper voltage? Are you checking between the 2 terminals for the solenoid or did you check from pin 2(pin 2 is the left one when the pins on the plug are pointed towards you) to ground? FSM wants battery voltage from pin 2 to ground. If you are checking between the 2 terminals you will not get a proper reading as the signal is a PWM signal, a multi-meter will not read this correctly.
Are there any shorts on the wire that is going from the solenoid to the ECM? What is the resistance of the VVT solenoid?