Hello and a warm welcome to Rootschat!
Do you have a copy of the 1886 marriage cert to confirm names & occupations of both fathers?
You can get a copy from the GRO
https://www.gro.gov.uk/gro/content/certificates/Login.aspThere are several possible Davids of around the right age, only 1 David R but he is in Carmarthen. There is this possible Richard but without details of father, it's guesswork
1861 Caeperson bach, Llanelly RG9/4113 folio 38 pg 12
John Thomas head mar 49 formerly smelter
Jane wife 40 b. Llanddarog
John son 18 labourer in copper works
William son 14 mason's labourer
Evan son 11 potter
Mary dau 7
Richard son 3
all born Llanelly apart from Jane
1871 5 Oxen St, Llanelly Rg10/5467 folio 18 pg 27
Jane Thomas head widow 51 housekeeper b. Llanddarog
William son 24 coal miner
Evan son 19 puddler at tinplate works
Mary dau 18 opening plates at tinplate works
Richard son 13 pickling at copper mill
all born Llanelly apart from Jane
Possible for Jane in 1881
5 Cemi, Hengoed, Llanelly RG11/5375 folio 98 pg 20
Thomas Jenkins head mar 46 colliery carpenter b. Llanedy
Ann wife 46
William son 21 coal miner b. Glam, Llan... (?)
Rhys son 19 labourer on railway
Robert son 15 smith at colliery
Jane dau 13
James son 12
John son 9
Margaret Ann dau 7
Gomer son 2
all born Llanelly except where otherwise stated
But as said before, you really need the marriage cert to be sure you're following the right people.