I have placed Joel in this family group based on a Remington genealgoy report from Pat Boyden.
Joel and his family are living at Waterbury, Washington Co., VT., in the 1850, 1860, 1870, & 1880 Federal Censuses.
In 1850 Joel & "Almira" are ages 31 & 32, and have a daughter Elvira, age 11. Also in the household are (presumed) in-laws Lyman & Sarah Hall, ages 67 & 65.
In 1860 Joel & Armina are 42 & 43, and have a son Homer E., age 7.
In 1870 Joel & Armina M. are 52 & 53, and it is noted that Armina is an invalid. Also in the household are Lyman & Sarah Hall, ages 86 & 82.
In 1880 Joel has remarried and has a wife named Rhoda. A stepdaughter, Minnie Rand, age 15, is with them.
One genealogy says he died 25 March 1891 at age 73.