I don't have a lot on this couple but have been looking at it because Josiah Tidball was involved in a number of chancery suits with my prime interest Charles Landon Carter who would have been a cousin of Josiah's wife.
Eliza as you call her was Elizabeth Carter who was born 1787 at Sudley in Prince William County, the daughter of John (of Sudley Carter and his wife Jane Hamilton. I do not have a death date for her. Elizabeth's grandparents would have been Col. Landon Carter and Elizabeth Wormeley.
John Carter was a half brother to my primary interest Charles.