It appears that William and Elizabeth split up, beteen 1822 and 1826, judging by ages of children of William's two families, see below


William Nicolson, b 1779, d 1867 in Bower, married to Elizabeth Nicolson m.s. Banks,
Children
Janet b 1805 b at Lochend in Dunnet
Brodie b 1810 in Dunnet
Helen b 1812 in Dunnet
Elizabeth b 1815 in Dunnet
Isobel b 1815 in Dunnet
Donald b 1822 in Bower

in 1841 at Alterwall in Bower
Jannet Nicolson 25 Agricultural Labourer
Hellin 20
Isabell 20
with
Elizabeth Doul 11
William Doul 9
Margaret Doul 6
and
Elizabeth Banks 55

in 1841 William is less than a mile away at Lyth
William 40 Shoemaker
Jane 45
Catharine 15
David 10
Jannet 8
Esther 5
Sinclair 20 Agricultural Labourer Unknown

in 1851 at Lyth
William Head 49 Farmer 55 Acres 3 Lab Bower
Jean Wife 35 Farmer's Wife Wick
Caithren Dau 21 Farmer's Daughter Bower
David Son 19 Farmer's Servant Wick
Jennet Dau 17 Farmer's Daughter Wick
John Servnt 15 Farmer's Servant Bower

in 1851 West Alterwall
Elizbeth Banks Head 71 Formerly Farmer's Wife Bower
Jennet Nicolson Dau 34 Farmer's Daughter Dunnet

In 1861 at Lyth
William Head 59 Farmer 56 Acres 2 Servants Bower
Jean B Wife 65 Farmer's Wife Wick [ is this the same Jean, aged 30 years ]
Jannet Dau 28 Farmer's Daughter Bower
Esther Dau 25 Farmer's Daughter Bower
+
Anne Bruce Niece 10 Scholar Wick
James Rosie Servnt 14 Agricultural Servant Canisbay
William Nicolson Grnson 4 Dunnet

1861 at Alterwall
Elizabeth Nicolson Head 83 Pauper Bower
Janet Banks Dau 54 Agricultural Labourer Bower

1871 at Lyth
William Head 68 Farmer Of 54.5 Ac. Arable Bower
Jean Wife 74 Wick
+
Ann Bruce 20 Domestic Servant Wick
Margaret Sinclair 14 Servant Thurso
John Cormack 15 Servant Wick

William Nicolson b 1801, d 1880 In Bower

Elizabeth Nicolson, pauper, widow died 1867 at Aterwall in Bower aged 88, dau of Donald Banks, farmer
reported by her son Donald Nicolson