Your William Henry Richardson is probably (almost certainly) the William Richardson baptised 18 Feb 1827 in Leigh on Mendip, Somerset (adjoining Whatley), the son of Levi Richardson and Ann nee Peck. Levi and his family arrived in New York from England 6 June 1831. I think the 2 wives you have for Levi are wrong, although he did marry twice in Somerset and had children by both wives i.e. Grace George (died 1816) and Ann Peck.

Levi was the brother of my 3x great grandfather Benjamin Richardson b 1781 in Babington, Somerset, sons of Simon Richardson.

Brian