Thomasine BARRINGTON Hopton - Lineage is not correct

After Sir Philip Barrington the lineage is not correct.
Please, see here:
https://www.esah1852.org.uk/library/files/T2010000.pdf
http://www.tim.ukpub.net/barringtons/Barr.html
Sir Nicholas had by his wife Alice Belhouse four sons, Nicholas who succeeded him, Thomas, Roger, and Philip. Of Thomas and Roger there is not any trace; Philip married Margaret daughter of Sir William Tey; he was knighted and resided at Rayleigh, as did his son Nicholas who was keeper of the King's park there. This Nicholas married Margaret Cloville and had a son John, who was the last male representative of this branch of the Barringtons. He and his wife Thomasine were buried at Rayleigh, where there was formerly a monument to their memory. They had an only daughter, and heiress, Thomasine, she was thrice married: first to William Lunsford, of Lunsford in Sussex; secondly to William Sydney, of Penshurst in Kent; and thirdly to John Hopton, of Cockfield Hall in te parish of Yoxford in Suffolk;

Thomasina's parents are John Barrington, of Rayleigh, Esq. (died 8th of November, 1416) and Thomasina Totham (died 15th of September, 1420).
Please, see here:
https://books.google.nl/books?id=ioYuAAAAMAAJ&hl=nl&pg=PA72...
https://books.google.ca/books?id=Uhc5AQAAMAAJ&lpg=RA1-PA65&...
Johis Barrington, Armigeri = Esquire