Side Mirrors do not work

check the fuse for the rear window defogger

I had the exact same issue with my '04 Sonata. It is in fact the 15 Amp cigarette lighter fuse causing the failure of the side mirrors. If you noticed, there are no fuses for the side mirrors. You also mentioned one of the cigarette lighters works and one doesn't. Just replace that fuse for the cigarette lighter and you should be all set. You probably already figured out the solution, considering the date of the question. But felt my input could help anyone else with similar issues.