My wife is of the the line you are working on. It descends from Jeremy Adams (1604 England), who came to Massachussetts with Henry Adams in 1632. They were probably brothers or cousins. Henry's line remained in MA and led to Presidents John and John Quincy Adams; Jeremy's line kept exploring and moving south. The confusion is that both lines contain a John Adams who wed an Abigail Smith. Our John Adams was 1637 - 1670 and Abigail was ca 1640 - ? President John Adams was (1735 - 1836) and Abigail was (1744 - 1818). Our branch moved almost immediately from Braintree, MA to Newtown (Cambridge), MA to Hartford, CT to Huntington, Long Island, NY to Great Egg Harbor, NJ to Delanco, NJ, etc. Too much to detail here. Good sources are "Henry Adams of Braintree" (date?) and "Genealogical & Memorial Cyclopedia of the State of NJ" (1910) pp1586-1589 et al.