I am not a relative, but I have been doing research on the descendants of Alexander Hamilton, which would include Alexandra, Elizabeth and Pauline. The Hamilton family 'spokesman' Douglas H tells me that Pauline married a John McKee Shaw, but I have not found any corroboration of that yet. What I do know about this family is the following:
Paul Edgar - died 20 Jan 1953 in NJ, possibly Menlo Park as his veterans headstone app was submitted by the Superintendent of the NJ Home for Disabled Soldiers there.
Alexandra Schuyler Hamilton - sometime between 1930 and 1935 was admitted to the NJ State Hospital, a mental asylum in Trenton. She appears to have spent the last 40 years of her life there, dying in July 1975.
Elizabeth - last info I have on her for sure is her enrollment at an Episcopal School/Home in Helmetta, NJ in 1940.
Pauline - she attended the same school with her older sister. Then, a few months after Paul's death, I think I found her returning from England in April 1953 aboard the French ship SS Flandre, apparently alone. I also have a couple hints of her death in Jun 1971 as Pauline Shaw, but until I can corroborate the marriage, I don't know for sure.
Hope this helps.