The parents of Jane Cooper are unknown. She was the sister of John Woollen not his daughter.
"2 Nov 1642 "Itt is ordered thatt if their be any goods due to John Woollen in the marchants hands in reference to Delaware Bay, there shall be 3l detained to secure a debt to Mr. Bryant of Milforde till things be cleared betwict John Woollen and him."
The earliest sources we have of Jane and John are in Connecticut. There is no documentation of their past in England.
I have moved John to be the brother of Jane and detached John from the parents currently attached to him. John Waller Woolen, I and Isabel Woollen