Given the question marks over the likelyhood of the James Broatch, blacksmith with wife Elizabeth Paterson, I wonder if you have come across this entry:
1851:
Isabela Broutch 63, Blacksmiths Widow b. Dumfries, Dumfriesshire
Peter Broatch 30, son, agr. lab. b. Holywood, Dumfriesshire
Robert Miller 34, nephew, Pauper Cabinet Maker b. Abbey New
Charles Miller 10, nephew's son, b. England
Thomasina Currie 10m, niece's daughter b. Dumfries, Dumfriesshire
Address: Nethermill, Kirkmichael, Dumfriesshire
And in 1841:
Isabella Broatch 50, independent
Peter Broatch 20
Agnes Broatch 15
Address: Nethermill, Kirkmichael, Dumfriesshire
I see from one of your previous posts,
www.rootschat.com/forum/index.php/topic,429233.0.html that in one census for George there is a possibility that George's birth place may have been Kirkmichael, as discussed with Gadget on that post - could fit with the above if you are able to confirm further.
Isabella is still living in Nethermill Village in 1871 with her son Peter and a granddaughter (think g/daughter is daughter of Thomasina Currie who showed earlier as a niece to Isabella) - you could perhaps check her death cert if she died in Scotland (possible entry showing for on SP), to confirm her husband's name and occupation. Or, alternatively, you also have Peter Broatch's death to check to see what it says regarding his parents.
Monica