you will have to add the code to kill the session to a page on the www.mydomain.com site. Here's one way it could be done:
on the checkout_success page, add a Continue shopping link:
<a href="http://www.mydomain.com/catalog.php?clear=1">Continu Shopping</a>
the clear=1 query string variable can be used to trigger the kill session code.
<?php if(isset($_GET['clear']) && $_GET['clear'] == 1) { ?>
<Kill session code>
<?php } ?>

