I found them! I had a flash of inspiration this morning - they are listed with surname 'Eddie' rather than 'Adie'. The entry is as follows:
Walters Wynd, Hawick
John Eddie - Head - Married - 58 - Woolen framework knitter - Lanark, Glasgow
Jean Eddie - Wife - [blank] - 59 - [blank] - Roxburgh, Hawick
William Thomson - Step son - Unmarried - 24 - Woolen framework knitter - Roxburgh, Hawick
Isabella Wilson - Step Daughter - Unmarried - 18 - Woolen factory worker - Roxburgh, Hawick
Jennet Wilson - Step Daughter - Unmarried - 15 - Woolen factory worker - Roxburgh, Hawick
John Eddie - Grandson - Unmarried - 8 - Scholar - Roxburgh, Hawick
John Thomson - Step Grandson - Unmarried - 16 - Woolen factory worker - Roxburgh, Hawick
William Thomson - Step Grandson - Unmarried - 18 - Woolen factory worker - Roxburgh, Hawick
Jane Thomson - Step Granddaughter - Unmarried - 14 - Woolen factory worker - Roxburgh, Hawick
There are also details of 1 servant and 19 lodgers - I can give you the details of them if you like. It must have been a large house!
So, from the above, it looks as if Jean has a child William with her first husband. Is this the same William as you though was the son of Francis Wilson, or is it second one? In fact possibly more than one son with William Thomson, given the 3 grandchildren with the surname Thomson. It also looks as if she 2 more children with husband Francis - Isabella and Jennet.
I still can't find Jane or Elizabeth on it. It is possible that Elizabeth and Robert had emigrated by that point, or had left Hawick at the very least.
Have you tried looking at the 1871 census for the family. You can see it at www.scotlandspeople.gov.uk
. It is a pay per view site and will cost you 6 GBP for 30 credits. 1 credit to biew a page of search results, and 5 to look at the image of the entry, which you can then print off. You shouold managed to narrow things down quickly as Adie/Eddie is not common in the 1851 census in Hawick, so I doubt there will be many more in the 1871 census.
I will keep digging away here - let me know how you get on.