I have had this same issue and have read of other apps that appear "duplicate" times on device in other forums too (this being one of the forums). I only know of two ways to resolve this:
1. Deregister and Reset the device (a lot of work and not sure if this will permanently fix in future);
2. "Hide" the unusable icon. Go to Edit Profile -> Manage Content -> Apps -> Deselect the unusable icon. If you select the wrong icon, just go back and select the other one since the tune in app probably looks the same. It did on mine.
This appears to occur after an update is installed and the "older" version sticks for some reason. Hopefully B&N will fix in future.
I've done both methods above and they do work but are more of a work-around, especially the second option.
Hope this helps!