The mother is Margaret McNamara, born Crusheen c1840.
The eldest child, Patrick John Butler, was born in Loughanabrone, Crusheen 1873 (I have his birth record). Soon afterward, the family moved to Liverpool, England where Susan Butler was born in Liverpool c1875, and Michael Joseph Butler was born Liverpool c1876.
Margaret's husband, Michael Joseph Butler (born Crusheen c1840), seems to have come over with them to England, had the two younger children, and died somewhere between 1876-1881. As he was a docker and mariner, it's highly likely he drowned at sea.
I don't have them all together on a census I'm afraid. I know for certain Margaret was illiterate, so I'm not really surprise they didn't appear when the children were young, particularly after her husband died.
The only census's I've managed to find any of them in are the ones for 1901 and 1911. In the former, Patrick is living with his mother, Margaret, in Hill Street. He's and insurance agent, and she's a housekeeper. And I have Margaret in 1911 living at Patrick and his wife's home in Devenport Street.
When the children were young, the family appear to have moved about quite a bit, and I was hoping the directories would enable me to pinpoint some of the locations so I can verify a miltary service record I've come across (hopefully) for Michael.
Regards,
Ann