I think your dates are wrong or you are missing a generation. John, born 1818, is unlikely to be a brother to Peter Franklin (born 1845) and Michael (born 1849) -- there is a 40 year difference in age.
Peter's marriage record in 1874 in Amesbury gives his parents' names as Martin & Kate. They were married in the Catholic Church in Amesbury -- getting a copy of the parish record might provide you with more information than what is included in the civil record.
I see from John's marriage record that he was likely born in 1838 (not 1818). He also names his parents as Martin & Catherine in the record dated in 1872 (married Bridget Rafferty in Amesbury by a Catholic priest).
1870 US Census
Baker, John, aged 40, works in woolen mill
Baker, Sabrina, aged 27, works in woollen mill
Baker, Michael, aged 30, no occupation
Baker, Patrick, aged 22, works in woollen mill
The 1880 census shows Michael as a brother living in the same household with Peter. The 1900 census shows Peter's birth date as May 1840 and Michael's as July 1841. Indicates that they immigrated together in 1867.