how do I change the url based on a theme?
Normally, you could accomplish this with URL rewrite rules or theme switching modules like ThemeKey but you're moving to a different sub-domain which Drupal is going to assume is a new database. The best way to do this then is to use the Domain Access module to simulate the use of a sub-domain without switching your database. 

Domain Access is a little trickier to setup (read the install file carefully) but it allows separate themes for each subdomain with the "Domain Theme" module.


  Domain Theme -- Allows separate themes, theme settings and colors for
  each subdomain.