Returning to the marriage of John and Jane Williams at Llanerchymedd in 1848, I've searched for more information on their parents. Assuming the 1841 census previously posted for Jane with father Evan is correct, there are a series of baptisms (but not Jane's) which show that her mother's name was Catherine.
Baptisms at Ceidio/Rhodogeidio with father Evan Williams, a Winnowing Machine maker (and Innkeeper in 1817), mother Catherine, living at Llanerchymedd:
John - 28 Sep 1817
Grace - 25 Feb 1820
William Morris - 15 Nov 1821
Thomas - 29 Oct 1823
It seems Jane also had a sister Anne as there is a marriage:
Anne Williams, f, s, of Llanerchymedd, Llechgynfarwyd, dau of Evan Williams, machine maker married Bennett Jones, f, b, mariner of Llanaber, Merioneth, son of Evan Jones, master mariner at Llechcynfarwy Parish Church on 17 Mar 1840.
I believe the Richard Williams (15) mentioned by despair and living in Twrcelyn St. Amlwch in 1841 with mother Grace and siblings Hugh, John and Henry is 'our' Richard. I cannot find the 1851 census despair reports "but he's still there in 1851", but mother Grace (68) and John (24) are at Market Square, Amlwch in 1851.
The marriage of a Hugh Williams (below) suggests the deceased father was named John.
Hugh Williams, f, b, shoemaker of Twrcelyn, Amlwch, son of John Williams, shoemaker married Ann Thomas, f,s, of Llanerchymedd, dau of Robert Thomas, shoemaker at Llanerchymedd parish church 30 Oct 1846.
It seems that Catherine Grace was named after both of her grandmothers.