Onclick / Onsubmit Radio Buttons

Button still works great but I have an additional issue that is related. Been searching around the internet without avail, maybe you have some additional suggestions.

So a user clicks on 'submit order' and it disapears. Works good, no double orders. BUT... the user decides (after clicking on 'submit order') that he wants to change it, or edit his contact information. While the form is processing (before the next load page), he presses 'modify order'. This button is here for users to change there information if it is not correct. But when a user clicks on it AFTER the submit button it still proccesses the original order, and allows them to resend the order after they have made changes. Thus 2 orders go through for the customer, and we have to issue refunds.

So enlight of this, my question is, is there a way to additionally hide BOTH the 'submit order' button AND the 'modify information' button at the end of the form, no matter which one they pick?

Here is the code:

<input type="image" alt="Modify information" value="Modify information" src="WA_eCart/Images/Nautica/Btn4_EN_modifyinformation.gif" class="eC_ImageButton" onclick="document.location.href='checkout.php';return false;"/>
                        <?php if ($totalRows_rszipdestination == 0) { // Show if recordset is empty ?>
                        <input type="image" name="Submit_order" id="Submit_order" value="Checkout" alt="Submit order" src="WA_eCart/Images/Nautica/Btn4_EN_submitorder.gif" class="eC_ImageButton"  onClick="this.style.visibility = 'hidden';" />
                        <?php } // Show if recordset not empty ?><br /><br />

Any thoughts?