(If you use any portion of these notes, please give source credit to Lois Sorensen, Remington family researcher and compiler, and to other sources as noted herein.)
Daniel was "of Warwick." However, I don't see him listed in the 1820 census in RI. Could they have moved away and then back to RI before son Ben was born?
He may be the Daniel Remington, age 62, RI, laborer, living at Providence, RI, in the 1850 Federal Census. Daniel is living with Maria Waterman and three Allen family members.
I can't find any gravestone records for Daniel or Alice, or any death records. Perhaps Daniel died between 1850 and 1853, when the RI Death Index began.