Drupal 6: Allow external site to authenticate via Drupal
If you have access to the same cookies as the Drupal site, you can pull the session ID out of the SESS* cookie. Then check the sessions drupal table for the uid. 

The session cookie name is a little more challenging to predict as it is "SESS"+ an md5 hash of the session name from the host domain URL or cookie_domain setting in settings.php file. Given your full control over the site, it shouldn't be hard to work with that though.