So you must mean windows DVD maker!!??!
The drop menu for 'DVD burner' is where it should show both drives.
If it is only showing the internal one, i suggest looking at the driver settings for you external drive.
I presume there was software for it, not just drivers!? I would have a look in the software.
Also, does the external drive show up in 'My Computer'. If so does it show up as a 'DVD-RW'
If you have an internal DVD burner why do you need to be able to burn with the external one, as i would have thought that it would be slower....