On your Products_Detail.php page, the add to cart button populates the description that is used in the cart. On that page, you would want to find this line:
$ATC_itemDescription = "".str_replace(" ", "", $row_WADAProducts['ProductCartDesc']).(($totalRows_CartOptions > 0)?"--". htmlentities($row_CartOptions['CartOptions'], ENT_QUOTES, "utf-8"):"") ."";// column binding
Change ProductCartDesc to ProductShortDesc and the short description should be used.