New online order sends previous email receipt

My client has had a vexing problem we just diagnosed. After a customer completes an order and is directed to the checkout success page, Authorize.net automatically sends an order confirmation to the client and a receipt is sent to the customer. I have the system set up to send another email - more of a user friendly version of the Authorize.net email ("the Order") - to the client. Since we transitioned and I changed from a remote to local checkout, the Order has been coming after the initial Authorize.net notice, often significantly, like 24 hours or even several days. I finally figured out that the Order email is only sent when another new order is placed; it's one behind in the queue.

How do I correct this problem? I'm not sure which files to send you to take a look - please let me know.

Thanks - Joe