Scudder questions ?

My grandmother Muriel Freeman was the daughter of John Freeman of Brooklyn NY (Born Jan, 12, 1860)and Annie Scudder of Northport L.I. (Born Sept. 18, 1863) Her mother Annie was the daughter of Gilbert Scudder of Northport (Born March 4, 1839, Died March 27, 1892 in Norwalk, Conn.), L.I., and Nancy Barto ( Born 1840, Died July 7, 1875)of Northport, LI. Gilbert Scudder was the child of William Scudder of Northport, L.I. (Born May 1, 1810, Died Sept 18, 1850) and Ruth Enoch of Northport, L.I., William Scudder was the son of Moses Scudder of Northport L.I.(Born Nov. 20, 1778, Died May 1822)(I can't read his wife's name that my grandmoter wrote) Moses Scudder was the son of Edmund Scudder and Elizabeth Higbee both of Huntington, L.I., and Edmund Scudder was the child of Henry Scudder. I got this info from a paper my Grandmother filled out for the Daughters of the American Revolution. I am not sure if the dates are correct. She filled it out because she said there was a realation to Alexander Hamilton. This is what she wrote to them " I forgot to explain where the Hamilton's came into my family. I got the information form Capt. Ed who was realted to me on both sides of the house. His mother was Mary Hamilton and her father was Alexander Hamilton's son. My Grandfahter Barto's mother was Alexander Hamilton's Grandaughter, only she was Alexander Hamilton's daughter's child, her mane was Nancy Bishop, Captain Ed's Father was Andrew Scudder, my Grandfather's Brother on the Scudder side." Does anyone know if this is true ?