I'm going to try my hand at literary analysis here. If you take the Red Haired Man to be England (the Redcoats), the wife to be Northern Ireland, and the singer to be Ireland (from the Sinn Fein point of view), the song reflects the current political situation rather well.
The version I have is from the Boys of the Lough album "Wish You Were Here." Cathall McConnell, the singer, does the first three verses essentially the same as the version in the DT, but the last verse is completely different:
Oh my darlin' sweet Phoenix, if now you could be my own,
For the patriarch David had a number of wives, it's well known,
So yield to my embraces and straight put an end to all strife,
Or else I'll go crazy to gain the Red Haired Man's wife.
In other songs in the DT, I've seen "Phoenix Park" as a place name, apparently somewhere in Ireland. If someone could tell where exactly this place is, it might shed a little more light on the subject.
One problem I see with this analysis is that I suspect the song was written long before Irish independence--or perhaps it refers to an earlier partitioning of Ireland?
I'm going to submit this in another thread for further discussion.