im mostly following what you did.. sounds like you just bypassed the relay basically.. imho you should undo the wiring you did, and just tap a relay into the cigarette lighter outlet wiring, and run a constant power through it to the lights you want to be your DRLs

here is how i wired my overhead lights, you will basically do the same thing with your DRLs except that instead of a constant power from dash you will use the power tapped from the cigarette lighter

you only need to do one relay though, i had two because i had 4 lights, but one relay should be plenty to power 2 lights