Bit of a tricky one, and I can't answer all the questions but here goes:
An Agnes Calderwood married John Paterson 10/2/1815 Neilston, Renfrewshire and 3 children born:
William bp.1816 East Kilbride, Lanarkshire (this was Agnes' home parish)
John bp.1817 ditto
Isabella bp.1819 Neilston, Renfrewshire.
1841 Census - Seedhill, Paisley Low, Renfrewshire
Agness Calderwood 46 Not born in county
William Paterson 25 Weaver ditto
John Paterson 23 Blacksmith ditto
Isabel Paterson 21 Cotton Throwster Born in County
Agness Hamilton 14 ditto
Jean Leitch 7 ditto
Margrat Craig 4 ditto
In 1851 Agness Calderwood 60 born East Kilbride, Lanarkshire is working as a housekeeper.
I should mention maybe that Scottish women often gave their maiden names on census, even though married.
She died as Agnes Paterson 70, widow of a farm servant, on 19/11/1860 at 11 King Street, Paisley, daughter of John Calderwood, Blacksmith (deceased) and Isabella nee Locke (deceased). Informant was her son William Paterson.
Question is: was Agness Hamilton bc.1827 actually Agnes' daughter or was she just raised by her and who were the other 2 children with Agness senior in 1841?
What doesn't help is that in Scotland illegitimate children can have the surname of their natural father even though parents never married. However, I cannot find an Agnes born in the timeframe whose mother was an Agnes Calderwood (or Paterson).
I did find an Agnes Hamilton bp.1827 (on familysearch) dau. of a James Hamilton and Mary Leitch which in view of a Jean Leitch bc.1834 with Agnes in 1841 makes one wonder if somehow these 2 girls are connected. However, this might just be a red herring as there were a few other Agnes Hamilton's bc.1827 in Paisley.
So, whether Agnes Hamilton was indeed the daughter of Agnes Paterson, nee Calderwood and a John Hamilton I have no idea. Certainly, Agnes Calderwood married John Paterson, had 3 children with him and sometime between 1819 and 1841 he died. She didn't remarry and although shown as Calderwood on 1841 and 1851 census (not an unusual occurrence in Scotland) she died as Agnes Paterson in 1860 at Paisley
Annette