Ok, I got the answer to my original question so I'll post it here in should anyone else need it. This is actually almost the same thing Jon suggested.
If you always want customers accessing
http://www.yourdomain.com/x-cart/customer/home.php to be automatically redirected to
http://www.yourdomain.com you could do the following:
Edit the 'customer/home.php' script and insert the line
if(empty($QUERY_STRING)) func_header_location("http://www.yourdomain.com");
right after the line
require "./auth.php";