I've seen this before, but I don't remember what caused it or how I got rid of it. Can you try scanning with with ADW Cleaner and Malwarebytes? Are there any new items in Programs and Features under Control Panel?
Behind every good computer... is a jumble of wires 'n stuff.
A couple more things to try: Since you can't delete the new, duplicate icon, try dragging and dropping the old icon onto the new one. If it deletes, then, Voila!, you're down to a single bin.
Also, try going to Services>Personalization>Themes>Desktop Icon Settings (located in right side column) and uncheck the Recycle Bin Checkbox if it is indeed checked. Click apply - or cancel, if it isn't checked..