I have got a Mulhall thread in my tree but I haven't developed it that much. You never know it just might provide a missing link. I seen in another msg that you mentioned possible move to USA. My William Joseph apparently came back the other way.
William Joseph Mulhall b.16 January 1837 Dublin, Eire m.Theresa McArdle
Mary Ellen Theresa Patricia Mulhall 10 March 1856 Liverpool,
William Joseph Mulhall Abt. 1858 New York, USA
John Patrick Mulhall b.b22 Apri l 1860 New York, USA
William Joseph Mulhall m Jessie Ballantyne in Liverpool 1884
If it fits I'd love to share information.