Suz, thank you so much for finding them in the 1861 (I can't find it on F-Search but will look again in the library tomorrow). Of course I erred in saying Catherine was the first child she was the second (of only two). The elder daughter Julia Symmonds Twemlow never married.
In 1881 Julia is b. Cark, 1901 Cark, 1911 Cartmel (same place really) and likewise Catherine is consistently b. Hereford. So the family clearly had firm ideas where each of them was born. And Richard Twemlow was definitely born in Cheshire. Given the listing you've given from 1861 I'd think the census taker misrecorded his notes.
I am still inclined to believe that Elizabeth was b. Brecon or at least lived there from an early age. We have a sampler where she has embroidered the alphabet and "Elizabeth Symmonds Brecon 1837".
Mazi, the marriage is a possible, I had to look up Much Cowarne to see if it was in Herefordshire or Breconshire. As i don't know the records situation in either place, what is the likelihood of getting other details such as parents's names for the marriage or an occupation? How would one look for a Brecon baptism?
On Elizabeth's 1858 marriage, her father is Thomas Symmonds, deceased, shoemaker which is Thomas's occupation in 1841 Brecon so I'm reasonably sure they are her parents.