My Maxson line is on my Dad side and I do not know of any Bartons in that line. HOWEVER, my mother's side also has connections to Westerly, Rhode Island. Those ancestors migrated to upstate New York, mainly Washington County, NY, and married Bartons. BUT those Bartons were from Massachusetts (they also lived in Vermont briefly). That being said, it is entirely possible that some of my Massachusetts Bartons migrated to Rhode Island and are related to those you mentioned. My Bartons in New England date to the very early 1600s and may have come over individually before the major migrations in the 1620s and 30s. I can place them first at Cape Porpoise in what is now Maine. They were later in Salem and Framingham, Mass.