Hi Pip,
I think they moved to Blackburn, West Lothian, see the 1841 to 1861 census, ties up with the marriage in Bathgate.
In 1841 census at Savoy Street, Glasgow,
Wm Dawson 30 b 1811 Ireland Cot Spinner
Mary Dawson 30 b 1811 Ireland Cot Carder
Jean Dawson 10 b 1831 Lanarkshire
Mary Dawson 8 b 1833 Lanarkshire
William Dawson 6 b 1835 Lanarkshire
Jas Dawson 4 b 1837 Lanarkshire
Thomas Dawson 4 b 1837 Lanarkshire
Jean Dawson 60 b 1781 Ireland mother ?
Catherine Dawson 20 b 1821 Ireland Cot Piecer -sister?
Margt McGhee 2 b 1839 Lanarkshire
In 1851 census in Blackburn, West Lothian,
William Dawson 40 b 1811 Ireland Cotton Spinner
Mary Dawson 39 b 1812 Glasgow Cotton Piecer
Jane Dawson 20 b 1831 Glasgow Cotton Piecer Sister
Mary Dawson 18 b 1833 Glasgow Cotton Spinner
William Dawson 16 b 1835 Glasgow Cotton Spinner
Thomas Dawson 14 b 1837 Glasgow Cotton Piecer
Alexander Dawson 10 b 1841 Glasgow Cotton Piecer
Sarah Dawson 3 b 1848 Livingston, West Lothian
In the 1861 census in village of Blackburn, West Lothian,
William Dawson 48 b 1813 Fermanagh, Ireland Chemical Works Lab
Mary Dawson 45 b 1816 Derry, Ireland Lab Wife
William Dawson 22 b 1839 Glasgow Chemical Works Lab
Thomas Dawson 20 b 1841 Glasgow Chemical Works Lab
Alexander Dawson 18 b 1843 Glasgow Chemical Works Lab
Sarah Dawson 14 b 1847 Blackburn, West Lothian Cotton Mill Worker & Scholar
Ann Dawson 12 b 1849 Blackburn, West Lothian
Henry Dawson 9 b 1852 Blackburn, West Lothian
Alexander Dunlop 5 b 1856 Blackburn, West Lothian Grandson
Tom