All the following info was sent to me by Sherron Westerfield (sherronw@searnet.com).
Her name means "Olive" in English.
When she married Cornelius she was the widow of Garret Janse Cowenhoven (son of Jan Gerritsen Van Couwenhoven; b.1676 in Brooklyn). She had been his second wife.
Aeltje had a son by her first husband, Jan "John" Gerretse Cowenhoven (named for his paternal grandfather), identified in his father's will, 16 Apr 1711 (NYHS Will, Vol. 2, p.121). "Garret, son of Jan Gerritsen Van Couwenhoven," named his wife Aeltje and "my son, Jan." This rules out the possibility that there were other children born to that marriage. He left his wife and son "all estate real and personal, either in Kings County or elsewhere. My executors, if they see cause, may sell all my houses and land at Bushwyck, in Kings County. I make my wife and my brother Necesimus Covenhoven, and THEODORUS VAN WYCK [Aeltje's brother] Executors." Witnesses: Aris Johnson, Jacobus Simensen, Henry Filkin.
And even more importantly: "PROVED Nov. 3, 1712. ALTIE COVENHOVEN being then the wife of Jacobus Cousine...." see Abstracts of New York Wills (Lib. 8, p. 275)
Jacob Cozine, Aeltje's second husband, appointed Abraham Van Wyck, son of Theodorus, one of his executors. These two connections with the Van Wyck family support the idea that Aeltje was a Van Wyck.