To clarify: Sarah (Hawes) Shaw is said by the Society to not be the daughter of Thomas Hawes of Yarmouth?
If that's true, forget about Thomas of Yarmouth, and Yarmouth in general. Start fresh with your Sarah Hawes and work backwards to find her death record and marriage record if you don't already have them. Look for the *original record* not an index item. Look for more information about her husband and children as well. The children's later census records and birth/marriage/death records may suggest where she was born. Follow her husband back to his origins to see where to look for further evidence for both of them.
Your profile for her husband suggests that you know when he died, though you don't provide a source. If so, look for a will in the location where he died. He appears to have died before his wife, so she should be mentioned in any probate records for his estate. Also look for any land records that the couple may have produced. Any document along the way might provide that one clue to her origins. Or not.
When searching for records for Sarah, be sure to look also for surname variations: Hawes/Howes/House. All are common in New England. And above all, don't fall into the trap of assuming that a match on a name is the same person, we've all done that at least once and it leads you into bad places in genealogy ;)
