Bilbocious:
I know that I somehow have to use PWM and a 100K resistor because of the impedance.
I don't think that is an option. The device will be detecting the variable voltage produced on the centre pin of the potentiometer as the knob is moved.
You need to replace the manual potentiometer with a digital potentiometer of the same value. Then the Arduino can control the digital pot.
Alternatively replace the motor controller with one that can take PWM signals from an Arduino.
Or (if you like Heath Robinson / Rube Goldberg) you could use the Arduino to operate a servo that rotates the knob.
...R