Isaac Southworth - Correction of the parents of Isaac Southworths children

Isaac married Abenaide "Ida" Smith in Alabama in 1819, almost a full year prior to the birth of the oldest child, William Smith. Thus all the childrens mother is Ida Smith. While applying for the Mayflower Society, I and another researcher spent months trying to find out this information and in particular who was Agusta Carpenter. There are no records of this person other than some family trees without sources.