The version of "The Red-haired man's wife" in DT is incomplete. Jon W's verse is the last of 7 of a copy in Colm O Lochlainn's 'Irish Street Ballads', #97.

This seems to be no relation to Katherine Tynan's song. There are three versions of the tune in the Stanford-Petrie collection, all collected before 1867.

The song doesn't look much like an allegory to me.