For bad stains with brake dust in them, I've started using acid as it will take it off right away. The clearcoat won't be attacked if you wash it off within a reasonable amount of time. You could start with a very mild acid like vinegar, but it may not be strong enough. Personally, I use muriatic acid (HCl solution) and just leave it a short period of time.
This is a 20+ year old disc brake dust shield I could not get clean even sandblasting it, or any chemical cleaner. The car had high-dust Jurid pads on it and the brake components had a baked-on coating that was impenetrable. Acid cleaned it in a few minutes and then I refinished it with high-temp paint. I did the calipers the same way, too.
I "painted" the acid on and it amazingly just wiped right off, a little bit of abrasion with the brush bristles was all. I've done the same thing on clear-coated alloy wheels that were terrible and it works great.