I am not positive, but I think he is the A. J. Remington, age 35 b MA, living at Clark, WA, in the 1870 Federal Census; and also the Andrew J. Remington, age 46 b MA, living in Clark, WA, in the 1880 Federal Census. I cannot locate him in the 1860 census, so perhaps he was on the move. The names of his two children may be clues to his family of origin. In any case, I am including this marriage and the children here, pending further research to confirm.
According to Lois Remington Smith in "The Remington Family" p. D-2, Andrew's wife Ellen died at Vancouver, WA; so this seems to confirm the above information.