I’ve done a couple of circuits like this in my house. You will need two add on switches to make the GE solution work. The install would be as follows:
- Assume whiteis neutral, black is hot, red is traveler.
- At the power source, connect line, load (both blacks in the box) to the switch. Connect red to the traveler and white to neutral, all on the switch.
- At the next switch, you will wire nut the two blacks that you pull off the old switch together and bury in the box. You will connect both whites and both reds to the add on switch.
- At the last switch, you’ll repeat step 2, though, there will only be one red and white.
Now, thinking this through for the relay…
The relay requires a constant source of power, so it will need to be in the first box. Then, the output for the relay will need to get to the light, so black and white will need to be capped off together all the way to the light. That leaves you with one red wire to achieve a 3 way style circuit for triggering the relay, which simply is not possible without an extra wire. I’m not an electrician though, so there may be others on here that have different wiring magic tricks that would work.