Your William that lived in Chester co. Pa. was the father of Meredith who moved to Frederick Co. Va.
This is how it looks:
William b.1690 in Ireland married Margaret ? b.June 1728, she and 3 children died at sea from smallpox on the way to America from Ireland. william died 10 Sept.1757.
Their children were: John, d:1815 in Moon twp. Allegheny Co. Pa he married Mary Bruce Meredith, d: in Frederick Co. VA he married Sarah Davis or David (from a Will) in1758 in Lancaster Co. Pa. William Jr.(I don't have info on him)
Sources: William's Will in Darlington File in Cumberland Co. Historical Soc. in Carlisle, Pa. Gen. of Darlington Family by Gilbert Cope, p.515 Tombstone: "Here lieth the body of Wm. Darlinton, who departed this life Sept. 10 1757in the 67th year of his age"