If Mary Jane Shaw was your gtgrandmother and her brother George Henry Shaw was gtgrandfather to Bob's wife then you share gtgtgrandparents (John Shaw and Mary Dakin) with Bob's wife which is what I said...I think...

Which would make you 3rd cousins.
http://www.genealogy.com/16_cousn.htmlAs for Mary Dakin what I have is that she married John Shaw and in 1861 they are together:
John Shaw,head,40
Mary,wife,34
Joseph,son,11
John Saml,son,9
Elizabeth,dau,7
George Hy,son,6
James,son,3
Mary J,dau1
By the 1871 census John Shaw has died (I presume) and Mary is remarried, surname Wright.
Mary Wright,wife,m,40
James Shaw,son,14
Mary Jane Shaw,dau,11
Martha E Shaw,dau,5
William Shaw,son,3
In the 1881 census Mary Wright is said to be a widow.
So, since you said you had information after 1860 I wondered if you knew who Mary Shaw nee Dakin married?
Have overlapped with Bob's post here ( I had to give inexpert advice to son on chemistry homework

) but I'll just leave my post as it is and hit the sack

Just found marriage registered at Bakewell Dec qtr 1870 Mary Shaw to John Wright. And if you think there are a lot of John Shaws then there are even more John Wrights
