An "Elizabeth" appears as the wife of John Hughes in the 1881 census. The same John Hughes was living with his wife Grace and the same family in the same place in the 1871 census, and one can follow them back through the 1861 & 1851 censuses below. There is no doubt that John Hughes has taken a new wife between 1871 census and 1881 census.
The only death entry that would fit is for Grace Hughes, died age 49, in Carnarvon 11b 396, in June 1875. A marriage (marriage certificate) took place on 4 October 1875 of a John Hughes (widower, aged 46) Elizabeth Hughes (spinster, aged 40). The address of both is Pen y ffridd, so it is definitely the right marriage.My assumption is that with his family health problems, John Hughes had the need to re-marry quickly to get a wife to look after the children. Note Elizabeth Hughes father is given as Griffith Hughes, copper miner, deceased.
So the Elizabeth Hughes of the 1871 census, living with her daughter Jane Thomas is the woman that is married to John Hughes in the 1881 census. And her daughter now reappears as "Jane E Hughes, unmarried, dressmaker, aged 16, born Llanddeiniolenon this census"
1881 census below
1871 census below
1861 census below
1851 census below
Possible first marriage might be John Hughes to perhaps Grace Thomas in June 1849 in Carnarvon 27 499
Jane Thomas 1864