James Shore m Sarah Richardson by banns on 18 Nov 1832, in Cheadle (about 4 miles from Stockport) - is this the right couple? witnesses George Smith and John Ridings, who witnessed most of the other marriages on the page too so probably aren't helpful to know.
The censuses for Jane sometimes give her pob as Nottinghamshire, sometimes Nottingham and once, Nottingham, Nottinghamshire. So I suspect she might have been born in Nottingham town rather than in one of the smaller towns/villages.
Too many surnames going on here for my poor addled brain! So, OP, you probably have this, but here goes:
Patience Rainsford bapt 1771, Dunham, Notts, parents John and Margaret.
Patience Rainsford m William Laughton in Tuxford, Notts, in 1794. Children (John and William) bapt 1794-96 as per Larkspur's previous post.
Sarah Betty Howe bapt Liverpool, 14.1.1803 (born jan 1802) to John Howe, button maker, and Patience (formerly Rainford) his wife.
I can't see a death for William Laughton between 1796-1802 either in Nottinghamshire or on the LancsOPC site. And I can't see a marriage for John Howe and Patience either.
Sarah Howe m Joseph Richardson in 1818 -- but in Manchester, not Liverpool. Both were single. Shame it doesn't give details for the marital status at the Sarah Richardson/James Shore marriage!
I looked for a death of Joseph Richardson in Nottinghamshire around the late 1820s-1831 period as well, in case Sarah was widowed there then moved back north, but nothing that might match.There was a couple, Joseph and Sarah Richardson, baptising (and losing) children in central Notts between 1822-1832, but with no Jane amongst them (and there's a possible matching marriage between the parents with a different MMN).