1. CAREY, John (d.1617), of Berwick-upon-Tweed, Northumb. and Hunsdon, Herts. (MP for Buckingham): HOP page does indicate two daughters. Somethings wrong with the two Anns, though. It feels like mixed data. I did an ascent approach and my data in Ancestry did match up with a Daniel husband as father of Clare, but that may be in one of the profiles, of which there should be only one, anyway. I am afraid to look, as the one profile I stumbled into doing the ascent, the possible husband was Darby! Not what I had. . ..
2. Wikipedia has this list of progeny, that's useful. I started working on one of the Ann profiles before I realized that another possible duplicate sister was sitting right there.
The Herald and genealogist, Volume 4, 1867 Google Books
- Henry Carey (Dec 1577 – Dec 1577)
- Henry Carey, 1st Earl of Dover
- Charles Carey, married Elizabeth Whitbroke
- Blanche Hunsdon (d. 6 November 1651), married 1) Christopher Peyton and 2) Sir Thomas Wodehouse 
- Anne Carey (bur. 6 December 1622), married Sir Francis Lovell of East Harlyng. The Wikipedia reference pedigree chart that lists this Anne married Sir Francis Lovell of E Harling in Norfolk (d. Nov 1624), s.p. So the Anne Carey who married other men or had children with them? Not so clear. . .
The Wikipedia reference also shows a different Anne Carey, daughter of Sir Edmund, married to Sir Wm. Uvedale also an MP (Hampshire, Newport, Portsmouth and Petersfield).
Any arborists might better tackle this one.