Sir John Hawkins (1532-1595) is credited with only one child, Richard (1562-1622). There are many Elizabeths in Hawkins lines, so you may have to do a lot of sleuthing. As suggested, she could have been the daughter of Capt William (1519-1589) who was the elder brother of Sir John (1532-1595). William had a large family and, while I haven't found a daughter, Elizabeth, she's entirely possible. 'Hope you receive somemore plausible replies.