Can I use this DPDT relay with this circuit? If so, which wires connect to what terminals?
According to the linked ad my comment was incorrect.

Input control signal voltage: 
0V - 0.5V Low stage (relay is OFF),
0.5V - 2.5V (unknown state).
2.5V - 24V High state (relay is ON).  &lt;-- It takes a 12 V control signal.
Input control signal high state current:
2.5V: 0.1mA
5V: 0.35mA
12V: 1.1mA  &lt;-- It will draw 1.1 mA on the control input.
20V: 1.9mA


You should be able to make it work.