I was thinking something similar as DrDiettrich. If the LEDs alternately blink, then replace the relay test circuit with the actual relay. Here's an updated diagram:
I'm a little concerned that the 2N3904 will not be strong enough to switch the relay coil. May need to replace with PN2222A or other.
EDIT: In the code, you may need to temporarily change the pulse interval from 40ms to 100ms to see the LEDs blink (pulse) a bit brighter.