I listened to the link and the 'trad tune' seems to be, as far as I can remember, the tune used for 'The Dark Eyed Sailor', but I can't see at the moment how it's connected with the Granny Mallie story.
The Shaun Davey 'Granuaille' is a superb setting of the story with some beautiful and dynamic singing from Rita Connolly on the CD.
Although a quick search on the net brings up a plethora of references to the history of this amazing woman and her family, there seems to be little interest as far as modern songs about her and her kin. The whole story is absolutely fascinating and should be a veritable feast of information to any interested writer of historical songs. The song posted here is a good start but I would want to get away from the connection with the well known 'Dark Eyed Sailor'. More on this subject please.