How to Wire This Latching Relay
I don't believe your application can be solved with the components you mention. Either you need switches that give a single pulse or a non-latching relay. My proposed solution is with a regular non-latching relay (and thus pin numbers may be wrong).

If  the relay is rated for 120V, then my first attempt would look like this. The below is with a non-latching relay though.







simulate this circuit &ndash; Schematic created using CircuitLab