Vibrating idling being caused by an electrical issue?

[NJX51981]

I had this issue, the vibrating idle while in park/drive, for about 15,000 miles now. I've brought the car in 3 times already, but they can't duplicate the problem.

I noticed a few days ago that if I turn off the radio, heated seat, and heat steering wheel it stops.

I have an 2005 X5 4.4i with about 50,000 miles. The dealer told me it was bad gas so I switched from Exxon 93 to the BMW recommended BP/Shell 93. No change in the problem. I had the injectors flushed--nothing.

It's very annoying. Sometimes the vibrating gets pretty rough and the RPM needle sputters. Not only that, my side view mirror glass (both driver and passenger sides) pan in and out when I accelerate.

What's the possibility that when using everything I'm drawing to much power? I replaced the alternator at approximately 30,000 miles.

Someone please help -- it's driving me crazy.