Looking further at Owen Williams and Elizabeth Williams, parents of Elizabeth (1859) etc, they were living at Pen Bryn Dona, Llanddona in the 1851 census, before their marriage:
William Williams, head, 66, farmer, b. Llanynghenedl
Martha Williams, wife, 45, b. Llanallgo
Elizabeth Williams, granddaughter (described as grandwoman), 18, House Serv., b. Llanddona
John Williams, grandson, 8, Bangor.
Owen Williams, Miller Serv., b. Pentraeth (his age looks like 35, it is transcribed by Ancestry as 2, I think 25 is closer to being correct, judging from later censuses and his age at death.)
Owen Williams died 6 Oct 1887, age 62, at Penbryn Dona, miller. Informant Hugh Williams, son.
Elizabeth is also living with her grandparents at Penbryn Dona in the 1841 census.
I think I have found Elizabeth's family. There is a baptism for an Elizabeth, dau of Hugh Williams and Elizabeth, farmer of Hafod y Rhyg at Llanddona parish Church on 24 Aug 1834.
Her siblings were baptised there as follows (all Hugh Williams & Elizabeth, Hafod y Rhyg):
Mary 25 Dec 1830; Anne 21 Feb 1836; Catherine 15 Oct 1837; William 7 Apr 1839; John 27 Sep 1840; Ellen 5 Oct 1842, Hugh 15 Sep 1844.
This family with their older children can be seen in the 1841 census at Hafod y Rhyg, Llanddona (on the next page from Pen Bryn Dona).
I can find some deaths registered at Hafod y Rhyg, spelt variously:
Hugh Williams, 78, 22 Nov 1885, farmer. Informant William Williams, son.
Elizabeth Williams, 81, 8 May 1892, widow of farmer Hugh Williams. Informant Hugh Williams, son.
John Williams, 37, 22 May 1878, joiner. Informant Hugh Williams, father.
Hannah Williams, 64, 25 Sep 1910, daughter of farmer Hugh Williams. Informant Hugh Jones.
I can't find the marriage between Hugh Williams and Elizabeth Williams.
I'll see what else I can find about Owen Williams (father of Elizabeth b. 1859).