Interference with wiring

That is a tricky problem. As I understand it, when you connect up a 12 Volt supply to a motor controller, that affects only one pot reading on an Arduino where the pot is connected to a separate 5 Volt supply. Is that right?

What connection is there between the 12 Volt and 5 Volt supplies?

Are all grounds connected?

Where is the code that reads the pots? Did you set the analogRead input pins to be INPUT?