I dont think they are the same child possibly Henry had passed by 1851.Carmarthenshire Registry Office are pretty good if you write that you are looking for the birth cert of Richard Davies born 1841-1843 Llanllawddog,Carms.And you only want the cert if the following details tally up .Father David Davies Occupation a Farmer ,Mother-Mary.Possible address Lletynest?Llanllawddog.Theyll search between two years .Give your telephone no as well.Wed never be able to get the ref no for this cert or any other Davies in Carms unless they had an unusual first name as Davies is so popular a surname.I doubt very much that there are two Richard Davies with the exact same details as those above. Worth a try anyway i cant see at this point what else you can do.Best Wishes Karen