You should not change the ShopSite Images URL or all of your ShopSite backoffice buttons will break. The problem you are seeing with the Remove button for coupons not being the custom one you selected in Preferences -> Store Text -> Shopping Cart has apparently been fixed in v8.1, because I don't have the same problem in my store. So you could ask your ShopSite reseller to upgrade you to the latest version and see if that helps.
FYI, when I was checking out your site I noticed that some of your pages and More Info Pages don't have .html file extensions, which causes my Firefox browser (v1.5.0.7, the latest version) to display the raw HTML of the page. You may want to fix this by adding .html to the end of all of your filenames. Here are some examples:
http://www.giftspecialistsinc.com/p-simgou
http://www.giftspecialistsinc.com/p-checra
-Loren