Controlling One Motor With Two Potentiometers - Possible?

  1. First come, first serve: the first pot in use overrides any input from the second pot.

You seem to have a completely incorrect understanding of the potentiometers. You plugged them into the Arduino. You loaded a sketch. You booted the Arduino. From that moment on, both potentiometers are in use ALL THE TIME. The value that you read from the potentiometer might indicate that it is centered, but that does NOT mean that it is not in use.

You REALLY need to do a better job with the requirements.