Change Theme for Different Pages

I’m building three websites, that are all using the same install of WordPress. I’d like to have one main site which uses a specific theme, then have two subdomains (a TLD will point to each), which each use their own theme.

An example of what I’m trying to do is at Gap.com. Notice how you can switch between Gap, Banana Republic, Old Navy, etc. The reason that I’d like to use the same install of WordPress for all three sites, is so that visitors can use the same shopping cart for all three, and the person adding/updating content only has to login to one install.

Any suggestions?