This is where I got to before my eyes gave up!
You have mentioned Gwen Ellen in the 1881 as daughter to Griffith Williams ~
RG11/5564/105/8 - Vron Deg
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Going back to 1871 (RG10/5714/70/7)
Tan y waen, Llanwnda
Griffith Williams, 28, slate quarrier, b. Llandwrog
Jane, w, 31, b. Aberdaron
Griffith, s, 3, b. Llanwnda
Gwen, d, 2 mths, b. do
Sidney Williams,female, relation, 18, domestic servant, b. Aberdaron
1861: RG9/4338/59/7
Penylan, Llanwnda
William Williams, 44, Ag Lab, b. Llandwrog
Ellen, w, 45, b. Clynog
Griffith, s, 17, slate quarrier, b. Llanwnda
Hugh, s, 15, do, b. Llanwrog
William, s, 12, do, b. do
Thomas, s,10, scholar, b. do
Edward, s, 8, do, b. do
And 1851 - as previous post.
1851 HO107/2515/188/12
Pen(y) lan ucha, Llandwrog
William Williams, 37, Ag Lab, b. Llandwrog
Elinor, w, 38, b. Clynog
Griffith, s, 8
Hugh, s, 6,
William, s, 4
Thomas, s,1
All children b. Llandwrog
I always take relationships with a pinch of salt until proven - my father referred to practically everyone in the village where I grew up as 'cousins'. Many of them were but very distantly!
Added - Caernarfonshire has the highest % of Williams of any county in Wales - it looks as if Sidney in 1871 might be related to Jane rather than Griffith!