Hi absey,
If you link the tabs with the session key it will do what you want it to do. Use the correct variable, which should be "zenid". You can use something like:
PHP Code:
zen_session_name() . '=' . zen_session_id() 
to output the session variable and value. Or you can just use zen_href_link and set the add_session_id parameter to true.

I also might try using POST and making each site a button to avoid people copying the links from the site tabs and accidentally emailing their session id. Could cause problems as it will log anyone in as that customer.