Hiya AH,
Welcome to Rootschat.
Scotland is the best place to research! Personally of all the UK it is by far the easier - but I am completely biased.
In general the census is the same in Scotland as in England and Wales. The LDS have not published the 1881 online
but I have it and have looked up your family. More in a moment...
THE website is
http://www.scotlandspeople.gov.uk/On here you'll find BMD for statutory registration for pre-1954 deaths, pre-1928 marriages, and pre-1903 births - All post 1855. It is a pay per view site but not hugely expensive a minimum of £6 but one cert = £1.20 (better than £7 in England).
All the OPR are indexed but not the images - they (in my opinion) are over priced to order the image - you often don't get much more info.
It also has the 1881, 1891 & 1901 census pay perview. You can get 1881 look ups here - quite a few of us do them.
Back to your family...
Is this them?
There is a Galston conection and the sibling names are correct but not the wife - could it be a second wife?
Dwelling: 40 Mc Intosh St
Census Place: Barony, Lanark, Scotland
Source: FHL Film 0203640 GRO Ref Volume 644-3 EnumDist 73 Page 3
James ROXBURGH M 45 M Galston, Ayr, Scotland
Rel: Head
Occ: Shopman Grocery
Joan ROXBURGH M 45 F Stevenston, Ayr
Rel: Wife
Mary C. ROXBURGH U 17 F Dalry, Ayr
Rel: Dau
Occ: Shopwoman Hosiery
John ROXBURGH U 15 M Old Monkland, Lanark
Rel: Son
Occ: Com Clark Cloth
Agnes G. ROXBURGH U 14 F Old Monkland, Lanark
Rel: Dau
James ROXBURGH U 13 M Old Monkland, Lanark
Rel: Son
Occ: Scholar
Joanna D. ROXBURGH 9 F Old Monkland, Lanark
Rel: Dau
Occ: Scholar
Jeanie B. ROXBURGH 7 F New Kilpatrick, Dunbarton
Rel: Dau
Occ: Scholar
Where did you get James juniors mothers name?
Also James' place of birth differs. But otherwise a good connection - What do you think?
Pam