If you are going to use dishsoap then use Dawn. It is the best at getting the waxes off your car. Professionals do use it too. Check out www.autopia.ws if you don't believe me.

You can use the Dawn to strip off the waxes you have on right now. That would be a good start. The next step should be to clay your car. If you are going to go through the work of the 3 stage wax job then at least do your car the favor of claying it down first.

The Meguiar's products for the three stage wax includes a cleaner wax that will get off whatever Dawn missed. No worries. The problem with waxes is that even the best wax isn't going to last longer than a couple months. 3 months tops. You aren't going to have to worry about striping it off because it will wear off all by itself. You may want to look into getting a polymer sealant first and then topping it with a wax. www.autopia.ws is a great resource if you need info on what kind of sealant to use. I'm partial to Klasse myself. There are several other members on this board who would agree with me there. Its very fine stuff.