I think you have your ideas all mixed up.
The reason you get a voltage on the signal wire of the potentiometer is because it is acting as a voltage divider for a voltage within the circuit board the potentiometer is connected to. That voltage is an OUTPUT. It would normally be connected to something else on the board that uses it as an INPUT.
Putting an external voltage on the potentiometer signal pin is like trying to get sh*t back into the goose.
Your external voltage must go to the thing that the potentiometer signal would normally be connected to.
The Arduino analogWrite() does NOT produce a varying voltage. It produces an output that is 5v for part of the time and 0v for the other part. The proportion of time when it is 5v varies. It is not a suitable substitute for the potentiometer voltage without other circuit components to average the voltage.
Even if you get a smoothed varying voltage from your Arduino it may not be suitable because the circuit board probably expects a potentiometer with a certain impedance.
SIMPLE SOLUTION ...
as suggested in Reply #1