I know this is an older post but if you are still looking occasionally I think that the relay is worth it and your problem is in two areas.
Why is the Relay worth it? Two reasons:
1. In this case its a fuse too. You are adding extra electrical stuff to your that could internally short. The relay/fuse provide a cutout so the $100 kit doesn't burn down your $55,000 car.
2. Using the "triggered" relay allows you options to turn it on and off.
Try this using the relay:
1. Trigger wires - If you attach them to the LCM its going to cause flickering and error codes, its very sensitive to resistance/voltage drop.
a. Instead: Pick one and run it through your firewall and attach it to your drivers side foot-well light (positive lead). This will power up/turn off the AE's with the interior lights.
b. If you want them to turn on/off with the headlights try attaching the other trigger wire to a positive wire that directly powers your headlights. Hopefully there is a OEM relay between the lights and the LCM and this will prevent it from setting error codes and flickering.
c. You can try "one" going direct to the LCM but most likely that's going to cause flickering and errors.
d. OR, if you are willing to have the AE's on 100 % of the time when the ignition is on then follow the directions here at step 4:
http://www.fastm.com/m3/angeleyes_orionv2.html
Yes these directions show an E46, not an E85/86 but in this case the wire and general location are pretty much the same. Its just an accessory positive wire. If you are apprehensive you can check it with a multi-meter. It should provide 12v only when the ignition is switched on.
NOTE: Stickmon is right: Per your wiring diagram you have two additional grounds located at the L/R angel eyes negative wire connections. Just connect the negative wires w/o grounding them to the body of the car. The only ground should be single ground wire at the relay.
This is my DIY - in it I sent the 2nd trigger wire to the fog light lead.
http://www.zpost.com/forums/showthread.php?t=724153
Good Luck