As the FORMER owner of a black car in the world's dustiest city, I can tell you that the Mother's Cleaner/Wax will not give you the results you are looking for. I detailed cars for a classic car broker, and some were pathetic when they came to me for work.
Here is what I recommend:
1. Wash with dish soap to remove the old wax.
2. Clay bar with a real clay bar, not that ICE crap.
3. Polish with a professional grade polish to get the swirls out
4. Wax twice to protect your hard work.
If your car is a daily driver, and it is exposed to all the elements, think about using a synthetic paint sealer instead of wax. If yours is a garage queen or a weekend warrior, use a carnauba wax.
Plan on working on the car all day.