You need two relays.
One relay to connect or disconnect the parallel arrangement.
One relay to connect or disconnect the series arrangement.
The relays must work together in break (the current connection) wait make (new connection) when the power changes.
It has to work this way regardless of going from 115 V to 230V or 230 V to 115 V.
The two anti-series zener diodes clamp the voltage across the relay coil to 120 V.
If the voltage is less than 120 V, the diodes do nothing, and the coli voltage is whatever is applied.
If the applied voltage is greater than 120V, the diodes clamp the voltage to 120 V.
So, no matter what voltage you apply, from 115 V to 230 V, the coil will see about 120V