Changing theme = change home page for mobile visitors?

You can make a simple function for this, check if is mobile (http://codex.wordpress.org/Function_Reference/wp_is_mobile). and redirect with wp_redirect() http://codex.wordpress.org/Function_Reference/wp_redirect

add_action('wp_head', 'redirect_mobile');
function redirect_mobile()
{
   if ( wp_is_mobile() ) 
   {
       wp_redirect( 'http://url' ); 
       exit; 
   }
}

This is untested but should work.
Add it to your themes functions.php file.