On this update order page you should already have the order info available to you from the existing recordset. So you could use the bindings from this recordset in the body of your email message to send the details to the address of your choice.
As for the user info for that order you would need to create another recordset on the page that would select the user record for that order. You can do this with a regular recordset that is filtered by the userID from the orders recordset.
Finally getting this to happen when you click on a particular button would require you to create a new form that has a submit button in it, you can use an image for the button. You can then just set the 'trigger' for your emailing script to be when that form is submitted to the page. In Universal Email this would be the 'submit button pressed' trigger.
