Searching for my connection to one of the original Van Dyck/Van Dyke families in the New Netherlands.

Is the information I have below correct?? I am unsure that my 6th great grandfather, Peter Van Dyke, is the son of Francis Jacobus Van Dyck? This is my weakest link.

I have more information about each of the couples below, but I am having a very hard time finding definite information about Peter/Petrus, including information about his wife Rachel Hudson and if he is positively the father of my ancestor John Van Dyke.

ANY helpful information is appreciated!

JOHN VAN DYKE b. 1775 in New York
m. REBECCA MORSE b. 1776 in New York

PETER/PETRUS VAN DYKE/VAN DYCK b. abt 1718(?) in New York
m. RACHEL HUDSON b. abt 1734 in New York

FRANCIS JACOBUS VAN DYCK b. 1683 in Long Island, New York
m. RESULE MONTRAS b. abt 1697 in Long Island, New York

JACOBUS FRANSZEN VAN DYCK b. abt 1652 in Holland
m. MAGDALENA CORNELISE EGMONT

FRANS CLAESSEN VAN DYCK b. abt 1613 in Holland
m. Immetje Dirks