Hi PSM ,
I am trying to find Sarah Dobson

Family Search - you can see has christenings for Thomas Dinny Dobson; Elizabeth Dobson and Sarah Dobson in Manchester with parents Richard and Catharine. (There is also a Rich. and Cath. in Liverpool- not the ones).
1841 HO107; Piece 575; Book: 15; Folio: 38; Page: 15
Holden Street
Richd Dobson 30 yrs Carter
Catharine 28 yrs
Thomas 1 yr
all born in county
This fits with the Thomas christening
Free BMD has a marriage 1838 Catharine Denny and Richard Dobson as possibles and this would support the strange christening name -Thomas Dinny Dobson.
Free BMD also has deaths which may apply: Elizabeth 1843; Richard 1846 and 1849.
There is also a birth for a Richard 1848 which makes things a bit strange when trying to sort out the deaths

**Just seen another Richard who may be the one born 1848.
There is also a Catherine Dobson death for 1852

That may account for why I can't spot them in censuses.
1861 RG9; Piece: 2914; Folio: 77; Page: 13
3 Coopers Court Queens Street Salford
Sarah Dobson 17 lodger yrs Cotton Spinner b Manchester
with a Hyde family
(possible?)
I've seen Thomas somewhere as a boarder/lodger but can't see them in 1851.