For example, let's say you're surfing MySite2/World - where $MySiteID = 'PX' - and you click the following link:
When World_Children/Can.php opens, I want it to inherit the $MySiteID value (PX).
Or if I visited MySite3/World - $MySiteID = 'Three' - and clicked a similar link, then the same popup (World_Children/Can.php) would open. But this time, it would assume the value $MySiteID = 'Three.'
It does look like your link is set up to do what you want. In your Can.php file, that value will be accessible using $_GET['MySiteID']