This Richmond family descends from the Mayflower Alden family according to this website.
The Seth Richmond family (minus Seth who died April 1842) is found in Euclid Twp., Cuyahoga Co., Ohio in 1850 with Nancy as the head of household.
1850 OH Cuyahoga, Euclid Twp
Richardson [sic], Nancy J., 43, b. OH
", Elihu, 19, OH
", Mary E., 17, OH
", Edmund C., 16, OH
", Martha E., 13, OH
", Laura, 10, OH
Elihu Richmond (Seth Richmond's father) was a pioneer of Euclid Twp., Cuyahoga Co., Ohio; he arrived in Ohio in January 1815, shortly after the close of the War of 1812, founding the "Richmond Settlement." His gravestone can be found here at findagrave.com.
Seth Richmond's son, Elihu Richmond, must be the Elihu in the GAR records who was born in Euclid, Ohio, and was living in Detroit, Wayne Co., MI, as early as 1875 [ City of Detroit Directory lists him as Richmond, Elihu, builder home 154 Sycamore and in 1884 was living at 576 14th Street, Detroit].
Excerpts from the J. B. Richmond book - Seth Richmond family (click on image to enlarge):
Other that the information provided in the J.B. Richmond book excerpts, I have nothing else on Nancy Pate Richmond or her children other than Elihu.