I happened to see your query about William Jenkins at the same time I found an old letter from an attic (really!). A quote:
"...One sister married a man by the name of Billie Jenkins, a blacksmith by trade, who went to live at [Glais, near Swansea, 30 miles from Carmarthen] and learned his trade at the Neath Abbey Engineering Works..." Billie Jenkins later emigrated "to the then-small Brooklyn of that date".
Could it be the same person? My letter-writer was quite vague about dates, but I know that a nephew of that Billie Jenkins was born about 1833, so Billie might have had a child in 1826. But why in Carmarthen? The letter-writer knew of two of Billie Jenkins's children, William David and Wennie, who went with him to Brooklyn, but of course there might have been other children.
The "one sister" is a sister of Griffith Hughes, b. Cadoxton abt 1801.