You can build the two charts separately, and use a parameter to allow the user to select which version they want to view. See: http://kb.tableausoftware.com/articles/knowledgebase/creating-sheet-selector-for-dashboard
Step one is building a parameter to select the four different values. Details on how to build a 'select measure' parameter can be found here:
After than then you can follow Matt Lutton 's sheet selector strategy. This is going to be the easiest strategy (building 2 sheets with perfect formatting) because I don't think there is a dynamic format axis available to switch you from % to $.
Also, here's a VERY simple example of a parameter with % and $ formatting, although I didn't bother adding commas, etc. There are lots of examples of this type of thing on the web.
I'll have to put that option in my tool belt, that solution may be useful to me as I am often throwing rates (1.3) and ratios (97%) in the vizes. I was able to get custom label formatting to work on one sheet.