This may help:
https://books.google.com/books?id=3MMBAAAAMAAJ&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q=Sarah%20Budd&f=false
There is a lot of research necessary, however, if you look at Budd, Purdy, and search for Underhill you may uncover the answers you seek.
I believe, if I recall correctly, this is the biblical record kept by the Irving family. The same said of Washington Irving. I believe if I read correctly, by his brother. There was something I glanced over about "Sleepy Hollow" and Rye, but that's it. It wasn't info I was looking into so moved on.
I think, based on my cursory reading of the info, is that there were three successions of Samuel Purdy. The I, the II, and the III. I believe the latter was an esteemed judge.
It is not unlikely that either a Sarah Budd or a Sarah Underhill would have married into the family. The Purdys were a respected family. The Underhills, you will find, often in this history of Westchester (as well as Rye), and most definitely the Budds as well.
Hope this information is helpful. I find it absolutely confusing how the author wrote it down, but a more learned/experience person might understand the lineage outlined in these family lines.
EDIT: The pages in question, in case it doesn't retain my search are 509, and 538 or 539.
EDIT 2: Please, if you find what you need to either corroborate or correct, use proper book citations. Calvin College provides a means for doing this called KnightCite, which provides you with every option you might need to cite a source.
