As per my other messages, I think Grisell was a full sister to Sir Thomas. Lack of wills and info on all children but going by parish records they seem to be full siblings.
The line for Diana to Andrew, from what I've seen is thus -
Diana's 3rd Grt Grandfather (Accidentally wrote 2nd Grt Grandfather previously)
John Brownell Boothby 1791-1850
Son of -
William Boothby of Bolingbroke, Lincs 1763-1845
Son of -
William Boothby c1730-1774
Son of -
Benjamin Boothby ?-?
Son of -
Thomas Boothby c1662-?
Son of -
Richard Boothby and Grisell Halford.
The generations of Benjamin and his father Thomas are vague and there may be another generation between them.
The sources given in the pedigrees I have see for Diana's line are -
'Evans, Richard K., The Ancestry of Diana, Princess of Wales, Boston: New England Historic Genealogical Society (2007), 214.'
'Roberts, Gary Boyd, The Royal Descents of 600 Immigrants to the American Colonies or the United States, Baltimore: Genealogical Publishing Co. (2008), 201.'
I'm personally not sure how good these sources are.