In the 1860 Federal Census, William & Mary J. Remington are living at Smithfield, Providence, Co., RI. They have four children: William J., Mary E., Jonathan, & Albert.
Apparently after his second marriage William & his wife Sarah moved to New Bedford, where they are found in the 1870 census. However, they are back in Coventry, RI by the 1880 census.
In later years he lived with his son Jonathan S. Remington at Greenville (Smithfield). He died at age 87, and the obituary was in The Evening Bulletin, Providence, as well as the New Bedford newspaper.
The birth record of son Charles gives William's birthplace as Warwick, RI.