There is an e-book that offers much of this family's information while they were in Connecticut, listing their younger children's marriages and affiliations with the church. It seems that "Farmington" is the parish.
This book reports Azariah and Ann Hudson as their parents, but gives no other clue as to earlier children or where they were at that time:
Memorial. Genealogy, and ecclesiastical history [of First church, New Britain, Conn.] To which is added an appendix, with explanatory notes, and a full index ... By Alfred Andrews ...
http://archive.org/details/memorialgenealog00andriala.
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