This is the family in the US 1880 Census, correct? I've posted the specifics from this census on Hannah (maiden?) Kitson.
1880 United States Federal Census [ACOM transcription, 2 Jun 1880]
Name: Hannah Kitson
Birth Year: abt 1854
Birthplace: New York
Home in 1880: New York City, New York, New York
Relation to Head of House: Wife
Marital Status: Married
Spouse's Name: William Kitson
Father's Birthplace: Ireland
Mother's Birthplace: Ireland
Occupation: Keeping House
William Kitson 36
Hannah Kitson 26
Sarah Kitson 4
Bella Kitson 2
George Kitson 2m [b Mar 1880]
This census has an excellent clue. The last child, George is detail as being born in March 1880. This pinpoints a place and date to look for a record that *might* have the mother's maiden name.
I didn't find a birth record indexed in any of the on-line resources, but that doesn't mean there isn't one to find.
I *think* this may be death record (index) for George Kitson (b Mar 1880), he doesn't present in the NY 1892 Census with rest of family, I presume he didn't make it. This record *may* have his mother's maiden name.
Kitson, George W, 4 m, 4 Jul 1880 #352642 , Manhattanhttp://www.italiangen.org/NYCDEATH.STM