I get a good feeling about your last note... It would explain why the name Frederick (Frederick Tremain) would appear as child of William Maurice..
I judge that Grandfather would have been born ca 1867 and i am pretty sure that his birthday was in January as was his wife (Mary Francisco Durham Randolph, actually, 1/3/?? and perhaps a year or so younger than he. The announcement of their marriage in Philadelphia identified him as William Maurice Randolph of NYC.
I don't think that i know of a George. I do know that there was 'Mary' (I don't know about the middle initial), Mary may have been older than William; ca 1865. Mary married Gaius Bolin of Poughkeepsie NY.
Absolutely a 'Russel', who i understand, died in childhood.
And also 'Alice'. I am not sure whether there were others or not.
I also recall from some papers, that grandmother Randolph left, that Grandfather had a very dear friend named Mr. James.. They would travel to Atlantic City and to Sarratoga, New York 'for the races'. If I am not mistaken, Mr. James bought "some land" in Atlantic City and tried to get Grandfather to buy some next to his.... Does any of this ring a bell with your mother-in-law, Mrs. James?
This is getting exciting... thank you so very much... Audrey