I am building a spotlight controller, and I have to wire 120v AC mains between two relays switching two spotlights. The run between the control box and the spotlights is about 50ft. Is this a safe way to wire this circuit?
Using the GREEN wire as a current-carrying conductor is a SERIOUS safety issue and Code-violation. Go buy some four-conductor (Red-BLK-Wht plus Ground) for the run from the relays to the remote plugs, which should be three prong outlets, not two like you show. Note that the WHT wire (Neutral) will be carrying the SUM of the two spotlight currents when both are on. The wire should be sized for the sum of the currents.
The green wire is insulated, and the same gauge as the rest of the wires. Does that make it any better?
Also, the spotlights have no ground connection, so it is really not needed.
In your application using the green as a common return line is fine. If the wire gauge is rated for the combined current of both lights there is no real issue to be concerned with.
Just think of the whole thing as being the same as if you had used two two wire extension cords and there never was a dedicated ground lead for either.