If you have bad water and want to continue washing your car at your home, you might should try the Mr. Clean kit...if nothing else because of the PUR filter that comes in the water hose attachment spray gun. Plus, you'll get the benefits of not having to dry the car. Just a FYI...the filter and soap that come in the kit is more like a trial size good for up to 3 washes. Stores that carry the kit also carry the replacement filters and soap refills which are good for up to 10 washes.
QUESTION: Does the spots come off during the next wash or are they stuck on there? If they're really on there good, get yourself a Mother's Clay Bar and follow the directions. It will likely pull the spots up and then you can rewax your car and start using the Mr. Clean kit on the next wash.