I just did a test on your site and i was not able to reproduce the issue, here is the steps i took:
1. on the home page i added one item, then clicked checkout, filled in the form and clicked the check out button
2. on the confirm page, i clicked on the home menu and added to the cart again, and then clicked check out.
3. the cart displayed everything correctly.
Are those the steps you are talking to reproduce this issue, if not, please let me know how i could reproduce this issue.
In regard to the shipping, you should clear the shipping cookie on the check out success page and on the top of your cart page.