Update - Im still not much further ahead in my quest to find Dorothys mother but.........
I sent off in the end, for Frederick George Robinson and Sarah Ann Berry's marriage certificate.
The certificate names Fredericks father as Joseph - correct
It has Freds date of birth spot on and sats Fred was residing in Bawltry at the time of marriage -which is only 11 miles from Gainsborough.
It also says Fred is a railway clerk/messenger, which is true on all the census results.
He was a batchelor according to the certificate.
So this probably is my Fred but is Sarah Ann Berry, Dorothys mother?

??
The marriage was 4 years after Dorothys birth.
Any thoughts appreciated.
Claire