Time Machine affects wrong external drive
The tmutil command should do the trick... in theory.

tmutil destinationinfo


should list the External HD and an associated ID string; feeding that string to 

tmutil removedestination (destinationinfo_ID_string)


should stop Time Machine from backing up there; and 

tmutil delete (path/to/the/wayward/"External HD"/backups)


should remove the backups from External HD--at least it did in 2012.