Help with servo and circuit board
Your circuit diagram is incomplete. You should trace the connections to all pins of the ICs. Some tracks may go under them, so use a multimeter on 'continuity test' to find where they go. Include all component labels, wire colors etc. 

You should also learn how to read designations, and search for datasheets based on them. U2 says '393' so it is probably an LM393 dual analog comparator (if it is then pin 1 should be connected to something). AQV252G is a 'PhotoMOS' relay. '385-25' is probably an LM385 2.5V voltage reference. Once you know what the parts do you can identify power supply rails etc. and lay out the circuit more logically.


  Should I try to use the circuit board? Or just scrap it and use the
  motor and pot directly?


It doesn't appear to do anything essential, so if you can't use the original controller then scrapping it and controlling the motor 'directly' may be your only choice. However the Arduino may not have enough processing power to control two of them, so it might be better to dedicate a separate MCU to each servo.