I doubt any regular car wash would take off hard water deposits that have been sitting there for a while. You could try a dedicated paint cleaner to see if that helps. For over the counter stuff, you would want Meguiar's of Mothers Step one products. If that doesn't work (and it wouldn't surprise me), you'll need to step up to a orbital polisher like a Porter Cable 7424 or 7336SP and some polishes like those from Menzerna, Poorboy's, Optimum, Pinnacle, etc. Of course, that is more for the detailing enthusiast. These machine are random orbit in nature, so they will not harm or burn you paint, even with a novice at the controls.
We have hard water here in Houston and the reason I refuse to install a sprinkler system is because of the water spots.