Switch between two themes, depending on what domain is used to access a site

mobile.php

<?php

/*
 * This solution assumes you've already set up your site so that the site domain is
 * your "normal" (non-mobile) domain, and your theme is your non-mobile theme.
 * 
 * In short, what it does it check to see if the site is being accessed through the
 * mobile domain. If it is, the mobile theme is used instead of the normal theme, and
 * all links point to the mobile domain (so navigatiion doesn't take visitors to the
 * regular domain.
 */


define( 'MOBILE_DOMAIN', 'm.mysite.com' ); // Whatever your mobile domain should be

if ( MOBILE_DOMAIN == $_SERVER['HTTP_HOST'] ) {
    // Override option table values for home_url and site_url
    // This way mobile users will stay on the mobile domain
    define( 'WP_HOME', 'http://' . MOBILE_DOMAIN . '/' );
    define( 'WP_SITEURL', 'http://' . MOBILE_DOMAIN . '/' );
    
    // Set up a filter to override the site stylesheet/theme for this request
    add_filter( 'pre_option_template', 'mysite_set_theme' );
    add_filter( 'pre_option_stylesheet', 'mysite_set_theme' );
}

// Override the regular theme with the mobile one
function mysite_set_theme() {
    return 'mytheme_mobile';
}