Cornelius Ackerman was my g-g-g-g- grandfather. I am descended from two of his daughters, Ann and Mary (via a cousin marriage in the next generation).
Cornelius married again in New Brunswick, and had the 3 children you list (Mary, Frances and Ann). His second wife was Francis Lawrence Vanderbilt, a daughter of Col. Richard Lawrence of Staten Island, who had previously been married to John Vanderbilt of Staten Island.
Did Elizabeth Blauvelt die in New York before Cornelius left for New Brunswick? We don't know; nor do we know anything of our distant cousins, descendants of the children of Elizabeth and Cornelius.