Ruth Remington is still living at East Greenwich in the 1860 Federal Census. With her is Almyra Briggs, age 48.
For the time being, I am making an assumption that she is a sister of Mahitable Greene, who married Dexter's brother Warren. Mahitable is a daughter of William & Elizabeth Greene. The death entry for Ruth says she is a daughter of William & Elza Greene. Elza may have been an abbreviation for Elizabeth. This Greene family needs more research.
If Ruth is in fact a daughter of this family, she may have been either a twin to Phebe, or else born in 1802.