Ali,
I just pulled out the Recorded lineage of the Richard Haines that is my 8X Grand Father and the names you sent me are on target with the exception of dates.
For all the others in this string as well, Here is what I know for a fact.
Richard Haines Sr. b-1636, m Margeret Abt-1658
There children that I know of:
John b- Dec 10,1664
Thomas b-Dec 22,1666 m-Elizabeth in N.J. USA
Richard Jr. b-1669 (My Ancestrial lineage)
William b-Apr 24,1672
Mary b-Jun 30, 1676 d-Aprox 1677
Joseph b-1682 on board the Amity