I had a "PROLUMEN" 6000K HID PRO kit on my 2000 XJ which I paid close to $500.00 CDN for. With that being said, I'm from Canada and I experienced the exact same issue as you did as I also have DRL's

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What would happen was, firstly, the lights would turn on automatically at full blast even though I didn't turn the lights on (which is what the DRL is supposed to do) but the problem was that the DRL unit only sent 50% power to the lights and it wasn't enough juice to power the lights so one of three things happened; Either the lights never turned on or one would turn on and the other would be dead or one would turn on and the other would flicker on and off.
My first solution: UN-PLUG THE STUPID DRL. - Your lucky, you don't live in an area where it is the law to have DRL's - Why would you want them anyway? Regardless, this worked.
My second and final solution: Get rid of the HID kit. The HID's caused me so many problems that it just wasn't worth it and I couldn't count on them every time I went out at night as they were inconsistent. I went a whole 6 months and they worked beautifully and then I started having issues, then they would work again and then they wouldn't and so on and so forth...
I hope this helps.
Oh and for some extra juice, I am running IPF headlights with GE nighthawk bulbs and the ARB headlight lume upgrade. Does the job and I've also got a set of Hella 500's on the front and it is more then enough light in black out conditions. The HID's were kind of ricer for my taste anyways.
- Thane