What would be the best way to setup a mobile theme for an existing domain with domain access module?
You need these two modules to do this:

https://www.drupal.org/project/simple_mobile_redirect
(detects mobiles and redirects them to pre configured paths)
&amp;

https://www.drupal.org/project/themekey
(serves any theme (e.g. a customized mobile theme) under any pre configured path)