Using 1 momentary switch to toggle between two latched states. Plus relay question
A bi-stable latching relay would be a simple solution.



Figure 1. Go to HomoFaciens and click "Start animation" to see how the pawl mechanism is advanced on every impulse of the relay coil.

No flip-flops, electronics or magic is required. Wire your button between the power-supply and the coil. Each impulse will change the state of the contact.

Imgur doesn't seem to like animated gifs.