Hello again John
1861 census living at 23 Cool Quay, Tirymynach, Montgomeryshire.
Richard Head Labourer
Harriet Wife
Abel son 1843
David son 1854
Edmund son 1840
John son 1851
Mary dau 1841.
I have had a look at the image and it shows MANAFON as John's birthplace, which rather confuses matters further doesn't it?
The village of Manafon (near Welshpool) is 14.5 miles from Mochdre

BUT, on checking the
1851 I found the family in Llanllugan (which is about 3 miles from Manafon):
HO107/2497 folio 43 page 10 - Upper Felling? Mill, Llanllugan, MontgomeryshireRichard Williams Head Marr 38 Fuller born Montgomeryshire Llanwydllen
Harriet Williams Wife Marr 40 born Montgomeryshire Berriew
Richard Williams Son U 17 born Montgomeryshire Llanwllchairan
Harriet Williams Dau U 15 born Montgomeryshire Mochdre
Edmund Williams Son U 12 born Montgomeryshire Mochdre
Abel Williams Son U 8 born Montgomeryshire Manafon
Thomas Williams Son U 7 born Montgomeryshire Llanllugan
John Williams Son 6 months born Montgomeryshire Llanllugan
Interestingly, two of the children were born in Mochdre.
I can see daughter Harriet in 1901 still in Pool Quay with her daughter Mary A, and in the 1871 she's still in Pool Quay working as a Servant for Edward & Elizabeth Jones. There's a couple of possibiilities for her in the 1861....both Servants.
Jan