Amongst the many threads below I don't THINK I spotted David and Alice's marriage record.
Given where they were living in 1881 (Pontypridd Reg District) I think this might be them, but Alice was indexed as MORGANS so it wasn't abvious. Individuals on the page are indexed in alphabetical order, so the pairs are not necessarily clear:
Marriages Jun 1879 Francis William Pontypridd 11a 483 MORGANS Alice Pontypridd 11a 483 Thomas David Pontypridd 11a 483 Williams Eliza Jane Pontypridd 11a 483
This info is from the FREEBMD site. Oddly I couldn't find this record on the FINDMYPAST site, which is meant to be the complete index.
Using the reference numbers above, I would suggest that you obtain a copy of the marriage certificate in order to clarify/confirm David's father''s name. Certs from: https://www.gov.uk/order-copy-birth-death-marriage-certificate
Given how difficult this family is proving to identify on the censuses, I think you need all the sources you can get to confirm, or refute, the info you've been givenfrom relatives.