Is there a marriage record available for Mary and Willam so that we can get a maiden surname for Mary?
Trying to identify a marriage has been frustratingly difficult. The earliest known son is David born around 1818. Mary was born around 1788, this gives us a large window of around 1806 to 1817 for the marriage. You can search on Findmypast for free for parish marriages (and look at the results)
https://search.findmypast.co.uk/search-united-kingdom-records-in-birth-marriage-death-and-parish-records/and_parish-marriages.
Results can be narrowed by “record set” e.g. Carmarthenshire marriages. There is also the possibility that if Mary was really from Glamorganshire then the marriage took place there instead. There is no marriage in Kidwelly or Llanelli (the obvious places given William in 1851 states he was born Kidwelly and in 1841 they are in Llanelly and children are born there). In the Glamorganshire records I can’t find a suitable candidate either e.g. one that may say William Williams of Kidwelly/Llanelly.
Another thing to add to the mix is that in 1817 Mary would have been around 29 and William around 36, so either or both could have married before and/or there are earlier unknown children. There is also a gap in the known births. We have
David 1818
John 1820
Margaret 1821
Sarah 1829
Martha 1832
So the gap between Margaret and Sarah could indicate Mary of “Glamorgan” was a second marriage that happened 1822-1828, which I haven’t investigated yet
