I'm going to have to buy the certificates for definate proof but Anna, thanks to your searching I think they have been found! I too checked the 1901 census with just V Williams thinking the name might have been spelt wrong but couldn't find anything. You are a super sleuth

I took a look at the info you found and on ancestry is shows the name as Vala, not a name I have ever heard of. Checking the document there is definately an i in there so as you say it could be Viola or indeed Vida!
I've also checked the freeBMD for deaths between 1901 and 1911 and in 1903 there is a death of a Jane Williams in Gower aged 37 and the death of David Williams aged 52 in Gower in 1904. Which going by their ages in 1901 would be about right.......
Checked marriages too, and there is a marriage in Dec 1890 between David Williams and Jane Thomas. Checked births for Jane Thomas and there is one in Gower in 1865, which would also tie in with the age on 1901 census....
I hope I am not getting ahead of myself with excitement! lol
kelly