in reply to your pm my friend, the best i can come up with is to get the marriage certificate for catherine's son james from
www.scotlandspeople.gov.uk it will give you his mother's maiden name and his father's forename. you can always post your results here for further help. there is no search result for catherine in 1861, so you can assume that she died between censuses. you might get lucky that she died after 1855, so there would be a death cert also on the above website.
james married elizabeth russel 10th sept 1866 at old monkland
in the 1861 census, james and elizabeth are already living as man and wife
1861 census; lanarkshire
james...head...age 40...ironstone drawer...born old monkland
elizabeth russell...wife...age 42...cotton weaver
catherine...dau...age 4
margaret frew...dau...age 20...cotton weaver
elizabeth frew....dau...age 13
james frew...son...age 10
all born airdrie unless stated otherwise
now elizabeth married hector turnbull june 1847 at new monkland
1851 census; browns knowes, gartness, shotts
hector...head...age 28...iron roller....born glasgow
elizabeth...wife...age 29...born coatbridge
catherine...dau...age 6
mary...dau...age 3
john...son...age 1 month
children born airdrie
1861 census; 76 johnston street, airdrie
elizabeth...head...age 40...cotton weaver...born old monkland
mary..dau...age 10
john...son...age 9
grace...dau...age 4
hope this is of some help my friend
remember and come back with your findings
Joe