I think you need to get the marriage certificate for Noah & Kathleen to find out the name of her father to be sure you have correct family.
If she is the Catherine Anne Price whose death was registered march qtr 1975 at Llanelli, her date of birth is given as 10 June 1905, so her birth should be registered june qtr 1905.
There's no likely birth reg for her in Llanelly. There's one registered at Neath
Catherine Ann Jones june qtr 1905 neath vol 11a pg 1030 mmn Jones
1911 census this Catherine Ann with her grandparents, but their name is Davies which doesn't match the birth reg
https://www.familysearch.org/ark:/61903/1:1:XWXF-WLYThis Catherine Ann in Resolven but mother's maiden name given as Rees on older sister Gertrude Mary's birth reg
https://www.familysearch.org/ark:/61903/1:1:XWXF-NHCAnother Catherine Ann, possible birth reg in march qtr 1902 for brother Edward John has mmn Jones
https://www.familysearch.org/ark:/61903/1:1:XWXF-QRGPossible marriage Edward Jones dec qtr 1899 Neath vol 11a with Catherine Jones on the same page
1901 census 16 James St, Neath RG13/5058 folio 65 pg 26
Mary Ann Jones head widow 61
Edward son 24 coal miner hewer b. Rhondda
Catherine daughter in law 27
William H grandson 12
Mary Elizabeth dau 8
Evan Jones boarder 20 coal miner hewer
all born Neath except Edward.
Census has 8 years for Mary Elizabeth but possibly it should be 8 months which would be a better fit for 1911 age. (I have a similar thing with my great aunt being noted as 7 years old when it should be 7 months)
At same address in 1911 - so is this Granny May?
https://www.familysearch.org/ark:/61903/1:1:XWXF-Q5R