The scant (and sometimes conflicting) information I have has come from books and other researchers, none of which I have personally verified. According to what I have found:

Captain William (sometimes called Robert) KIDD was born about 1645, probably in Greenock, Scotland. He died by hanging on 23 May 1701 in London, England.

William's father is claimed to be the Rev. John KIDD.
Nothing is known of William's mother.

In 1691 William married Sarah BRADLEY COX OORT in NYC.
Some sources claim that they had 2 daughters.
Daughter Sarah married Joseph LATHAM.
Daughter Elizabeth (who took the name of her step-father, ROUSBY) married a TROMP.

William's wife Sarah had 4 husbands. Her fourth was Christopher ROUSBY. Sarah had 5 children in all.

I hope this helps. I plan on doing further research as I have time.