Please note George Dalrymple (1710-64) could not be the son of John Dalrymple and Eliz Dundas since John Dalrymple died in 1707.
According to "The Scots Peerage" published in Edinbough in 1911, John Dalrymple (1st Earl Stair) and Eliz Dundas had 10 children: James b. 1670/d 1682 (accidentally shot by brother), John b. 1673 (2nd Earl Stair), James b. 1676 & Charles b. 1677 both d. young, William b. 1678, George (1680-1745) + 4 daughters. The focus should be on this earlier George whose grandson John (the 6th Earl of Stair 1749-1821) fought in the American war. He was a Captain int the 87th Regiment Foot.