You need to get the contents of the cookie from the request before WordPress sends any output to the response. At that point you can use wp-redirect to redirect the user to the desired site. You can use the “init” action to hook in before output is sent.
You may be better off to use plain php to build the splash page and do the redirects.
Note that duplicate content isn’t good for SEO, so you should be sure to flag one copy as the canonical version for any duplicate content.