Regarding the 3rd Baron's children: his will speaks for itself. There are a couple of transcriptions around on the net. Ironically, this is one time Burke's was mostly correct, as the will confirmed the data for all but one child.
As for emigration, you'll find the identities pretty well established in a combination of Augusta County, Albemarle County, and some notes as to who were the friends of the Earl of Gooch, then Governor of Virginia when these people arrived, in the governor's own records and those of his staff. Some of that is in the Albemarle County historical society, and mentioned in the tours of the Governor's mansion at Williamsburg. In the colonial records, Gilbert Campbell and certain others are listed as "Gentlemen"--a title that meant a lot more to the colonial authorities keeping said records than it does today. It meant the son of an armorial knight and lord, knight banneret (Baronet) or Baron.. "Esquire" was one more generation removed, not just an attorney. Richard Woods, the sheriff of Botetourt County and son of Samuel Woods (knighted in Marlborough's early campaigns)and Elizabeth Campbell is also listed as "gentleman." Peter Wallace, however, his cousin and brother-in-law is listed as "Esquire."