Margaret, I think your great-grandfather, Thomas Dunne, is also my great-grandfather. He was born to John Dunne and Eliza Mooney. I've forgotten the date but can find it if you haven't already filled in the missing info. (I realize this post is from over a year old) The Ballyhade connection is firm.
Thomas married Jane (Johanna) McGuirk. I remember finding birth certificates for their children, the oldest of whom was Patrick, my grandfather. He had a sister Elizabeth but there is a discrepancy in the date of birth. I have 1878 as her birthdate. Of course, it wasn't uncommon for a child to be christened, die and the name be used again for a later infant.