Hi Carolyn
Yes the only marriage does seem to be the one at St Peter & St Paul's in Ormskirk, Alice's parish Church as she was from Scarisbrick (then part of Ormskirk Parish). As many the locals were illiterate until fairly late in the 1800's the spelling of her surname would be down to the Vicar who officiated at the wedding.
The source was the North Meols Family History Society's Rimmer one name extracts from St Cuthbert's in Churchtown ( the Parish Church of North Meols). I have since bought a CD with a transcription of the 1813-1837 North Meols Parish Registers, and it confirms the details of the baptism for James Rimmer son of Alice Cooper baptised 22 Feb 1835.
I have Edwin as my 3rd Cousin 3 times removed so far, his father Hugh my 2nd Cousin 4 times removed. I'm also Selina Alice's 4th Cousin 3 times removed it seems.
If you have any more questions don't hesitate to message me.
Steve Baxter