Hello Annie,
I think the reason for your family uprooting themselves and heading for Liverpool could be down to Somerset having been severely economically depressed in the mid-19th century. Rural conditions were bad, and from the little I've read it's possible that the local quarries were getting exhausted.
George Mitchell of Montacute (nr Yeovil) was another man who made the move to the smoke. He was a young stonemason who in the 1850s moved to London and became a successful marble and stone merchant. He was also instrumental in setting up the National Agricultural Labourers Union. With a bit of sifting out of other George Mitchells you can find some stuff about him on the web, and there is a biography of him by Brendon Owen, though it deals more with him as a political activist than as a mason. But the early chapters do illustrate the appalling conditions that the rural poor endured.
(Some of my own family (they were in the gloving industry) went so far as to emigrate to the States at that time...)
As for the quarries, there's a bit of info in the Victoria County History for Somerset which you can access at
http://www.british-history.ac.uk/catalogue.aspx?gid=29. Stoke sub Hamdon is in vol. 3.
Also a bit at
http://www.wainwright.co.uk/history.php (Perhaps the intro of steam haulage mentioned there led to a reduction in the size of the labour force?)
Sorry that these really are only snippets of info. I wish I could help more, but looking for info about 19th century economic conditions in Somerset, let alone histories of specific industries, makes me realise how much really good info has been lost from the web since the 1990s. I'm thinking in particular of some really interesting articles on the Somerset gloving industry that I found then (I think it was in conjunction with an exhibition) but can't find now. Seems like a case of 'the book is dead, long live the book'!
Anyway, I hope this helps a bit. And good luck in your quest.
Birtle