Changing the color scheme based on the url visited

The Misconception

get_site_url() retrieves the site_url option from the database, as set under General Settings in the administrative backend / wp-admin.

If this is indeed

the exact same wordpress installation

it will always return the same thing, regardless of whether the location is reachable via one, two or five hundred domains.

You might want to check $_SERVER['HTTP_HOST'] instead.

if ( 'domain2.com' === $_SERVER['HTTP_HOST'] ) {
    $themeId =  "gold";
} else { 
    $themeId = "blue";
}

Real Voodoo

So far, your condition only works for the initial visit to your site.
Should you care for some real trickery and want the visitor to keep surfing your page under the initial domain: Check out this excellent answer by toscho.