First off, 'your' Selina who was married to Thomas Rule is definitely not the one who was dau. of John and Mary in Manchester 1841/1851 - that Selina was born in Manchester whereas 'your' Selina was born in Tattenhall, Cheshire!
As already pointed out, 'your' Selina Richardson was a servant in Birkenhead in 1851 (whilst the Manchester one was still in Manchester).
I have found 'your' Selina on 1841 census in Tattenhall, plus her baptism, and also her parents marriage - however, these are all in the name of Richards and not Richardson (don't know why) but by 1851 they have become Richardson and like Selina family are in Birkenhead.
1841 Tattenhall
Joseph Richards 35
Mary Richards 35
Ellenor (as transcribed but does look like that) 9
Dina 7
Ann 5
Joseph 18 months.
1851 Birkenhead
Joseph Richardson 44 Labourer
Mary Richardson 43
Anne Richardson 12
Joseph Richardson 11
John Bourker (?) stepson 22
Joseph Richards married Mary Bowker 8/10/1832 Tattenhall
Children:
Selena Richards bp.30/12/1832 Tattenhall, dau. of Joseph and Mary
Diana Richards bp.29/3/1835 ditto
Ann Richards bp.25/6/1837 ditto
Joseph Richards bp.28/6/1840 Tattenhall, son of Joseph and Mary (GRO index confirms mmn was Bowker).
Can't explain the change in surname, but Joseph married Mary as Richards, children born/baptised as Richards, 1841 Census Tattenhall as Richards - then family move to Birkenhead where they all become Richardson by 1851! In 1861 still Richardson.
Annette