Note from Marty Miles, August 2013 (lightly edited; for more information, see Sources below):
Captain Daniel Broadhead came to America with Richard Nicholls and the rest of the British when they took New Netherlands away from the Dutch and renamed it New York. Captain Broadhead was put in charge at Kingston. He wasn’t very well liked, and he died at age 30 in 1667. Not just sure how that happened. He had brought his wife, Ann Tye, with him, along with their three sons, Daniel, Charles, and Richard.
So there is poor Ann, in a strange country, no husband, and three little boys to take care of. So of course she did what they all did in similar circumstances: She found another husband. This time it was William Nottingham, who was a Lieutenant in her first husband’s Company of British Grenadiers. They had a son William and a daughter Elizabeth. Son William married Margaret Bergjen Rutsen, daughter of Colonel Jacob Harmen Rutgers and Marritje Hansen Bergen. (Yes, daughter of Hans Bergen and Sarah Rapalje!) Their daughter, Bregjan Nottingham married Andries DeWitt (Jr.), the brother of your Johannes.
I have more on Captain Daniel and would be more than happy to share what I have in my computer and what I can find in their files in the filing cabinet.
I expect you would be able to find lots in the History of Ulster County about him.
After Lieutenant William died, Ann found herself a third husband, Thomas Gaston. I don’t have any particulars on him.