While I am surprised by this behavior (I would have expected to only see the attachment that the user taps on) this is not hard to solve.
You can easily write a multipart MIME scanner that splits up a multipart message into the individual attachments.
Are you certain that you actually have individual files inside the email that is being sent? Inspect the raw message.
Also you might have set up your UTI registration incorrectly, please read my writeup: http://www.cocoanetics.com/2012/09/fun-with-uti/
Usually if you open an app via the File Open In (fom another app) you are getting passed a file URL that points to a copy of said file places in the receiving app's Document/Inbox folder. Inspect this URL to see what kind of file the system places there. If you don't remove it, then you can copy the contents of your app folder to the desktop with Xcode organizer.