David Stewart - Family of David Stewart (son of Lazarus)

What is the evidence his wife was Barbara Stewart (Hamilton)

Unless there are objections, i believe we should conform his family as described by Lew Griffin at http://www.lwgriffin.com/g0/p608.htm#i19454:

Family: Elizabeth (?) b. s 1730, d. s 1810

Children

1. David Stewart Jr. b. s 1754, d. 1811.
2. Thomas Hamilton Stewart b. 19 Apr 1756, d. 1838
3. Mary Stewart5 b. s 1758
4. Sarah Stewart5 b. s 1760, d. 1802
5. John Stewart b. s 1767
6. Lazarus Stewart of Giles Co. TN b. s 1770, d. 1830