Unfortunately, I haven't a clue. The entry in the Ela Genealogy only gives her name. One would suspect that she and Hannah were sisters - or cousins, since Israel and Edward were 1st cousins.
Here are the birthdates for the children:
Israel & Betsey:
Israel, b. 1770
Jonathan, b. June 24, 1773
Seth, b. 1776
Enos, b. ?
Jacob, b. 1784
Betsey, b. ?
Edward & Hannah:
Edward, b. 1780
Nancy (no birthdate given)
Wish I could be more help.