Well, thanks Matthew Edwards!
I appreciate your help. I have the Kennedy disk, which was mislablled and sent me by mistake. I am quickly out of my depth in talking about things Irish.
I listened a few times to the tune of "The Red Haired Man's Wife" in the digitrad. It does have a similar Mixolydian sound, it is sufficiently indistinct so that I could not sing it, and cannot say whether it is the same or not.
The words to "Red-Haired Man's Wife," in English, just sound dumb to me. Lyrical poetry often does not translate well, and I suspect I'd probably be more impressed if I could read the original. I do not think it is the same song, but I may not understand how songs evolve in Ireland.
In any case, thanks for spending some time on my question.