How can i turn a DPST button in to a DPDT?
Here is the equivalent circuit of the original switch, ignoring any presumptions about what it is connected to:-



simulate this circuit &ndash; Schematic created using CircuitLab
To reproduce its functionality with a single-throw switch and relay, do this:-



simulate this circuit
Diode D2 (which can be any general purpose type such as 1N4001) is required if the relay does not have a diode built in. It prevents switch contact arcing and EMI which would otherwise be caused by back-emf generated by the relay coil when it is switched off.