Hi,
Whilst I tend to agree that B Bellamy is in fact Rachel, the term brother-in-law didn't necessarily have same meaning then as today. He could easily have been married to a sister of Rachel's (he wasn't).
Furthermore, although initial is 'B', doesn't mean forename began with B. She could be a Betty, in which case her forename could have been Elizabeth.
What is puzzling, is why we can't find Thomas Bellamy in other censuses. Does anyone know where Brough Fen is exactly?
With regards Williams daughter, I think this should be Sarah J (not S), and she appears in 1871 and 1881 censuses. As you say, in 1891 she appears as Sarah J Doddridge (widow), with a daughter Jessie.
A Jessie Doddridge was registered 1889 Q4 Chesterfield 7b 763, but there does not appear to be a marriage registered for Sarah around this time. Of course if it was her second marriage, it wouldn't be under Thompson.
I suspect Jessie is illegitimate
Were you aware that William and Rachel had at least two other children, who didn't make it on to the censuses, both dying as infants:
Angelina Chr 25/5/1855, buried 8/4/1855 in Stilton
William Edward Chr 20/9/1857, buried 10/3/1858 in Stilton
Mike