Hi Dianne
Sancti has included some useful references for you to be able to follow up on. It does look likely that you may have some digging to do as you expected (which I am relieved about rather than this coming to you out of the blue....).
Not sure if you have carried out research in Scotland before and need some guidance for that. This is a useful guide here on RootsChat for you to have a look at:
www.rootschat.com/forum/index.php/topic,24468.0.html - Where to start with Scottish Research?
There is only one source for BMDs in Scotland and this is the pay to view site
www.scotlandspeople.gov.uk which although pay to view, the costs are reasonable. You can view images of certificates on line up to certain years (due to data protection) and after these cut offs, you have to order official extracts of certificates. For birth, the current cut off is 1910 (100 year rule). The cost of ordering a certificate directly through Scotlands People is £10GB. This fee is about to increase in a matter of days, on 1 April, to £12GB.
In your position, I would make ordering your mother's birth certificate my first start point and then start working back from there. There can be many twists and turns on research, and it is easy to make assumptions which can be wrong.
The marriage of Robert Russell and Jane Scott Jack can be viewed on line for £1.20GB (a minimal rise on this cost is also due on 1 April). Scottish certs in general are some of the best in terms of info and will give you all the info you need to be able to work back on their lines. There is a lot of resources generally available for research in Scotland for this earlier period which makes it easier.
For example, this looks a likely birth entry for Jane Scott Jack from IGI on
www.familysearch.org/Eng/Search/frameset_search.asp?PAGE=igi/search_IGI.asp&clear_form=trueJane SCOTT JACK born 26 Sept. 1856 in Bothwell, Lanark
Parents: James JACK and Jane CRAIG
A further likely entry for Robert Russell:
Robert RUSSELL born 28 Nov. 1855 in Bothwell, Lanark
Parents James RUSSELL and Elizabeth COWAN
The families for both show in the ealier censuses in Newarthill and are easy enough to find on the censuses. Would be good to confirm though first Robert and Jane's parents' names from their marriage cert to let you work back with confidence on their lines. Their families, from what I can see, look to be very much based in Newarthill as their parents also show as being born there on the censuses. This will be very much where the families' history lies together with a strong coal mining tradition. A lot of mining history in that part of Lanarkshire. There are a number of historical sites for mining in this area which will let you learn more about their lives and working/living conditions for later!
The Scottish 1911 census is due to be released on 5 April this year, which will help you further with the family.
Monica