I was just talking to my Grandmother, who told me that my Great Great Grandfather's name was George! Apparently he divorced his wife, and left their three sons and practically disappeared. She remarried several times and I now remember my Grandfather telling me about his grandmother who was an alcoholic and a gambler! The three sons were Robert (Roy), Frank and Jim. Frank and Jim both had daughters, whilst Roy had the three sons whose families I still keep in contact with, and am the only male Mehegan left. (The eldest son had a son and a daughter, with that son having two daughters himself, whilst the second had two daughters, and the third had one son - my father.)
There is still a possibility that there is another brother of George and Eugene, but I'm not sure.
I also found the record in the transportation records of a Robert and Hannah Mehegan (b. 1825 and 1834) coming to Sydney in 1857. They COULD be the parents of Robert (George and Eugene's Father) but this is just a guess. That name just keeps on seeming to pop up!