I am making an assumption that "Tripheny Peckham" age 89 in the 1850 census, living with Benjamin & Mary (Peckham) Remington at Newport, is Mary's mother.
According to a family tree at Rootsweb's Worldconnect, she is Tryphena Stockman, b 9 Sep 1763, d 16 Feb 1851, md 19 Nov 1786, d/o Jacob Stockman & Ann Wilbur (ref. Everett Cook). This information on her maiden name and parentage (not the dates) has since been confirmed by a Remington Family manuscript at the Newport Historical Society (Frederick C. King Papers) which reference the Peckham Genealogy by Stephen Farnum Peckham.
Abt 1763 - 1851 (87 years)
d. 9 Mar 1868, Newport, Newport Co., RI