Hi Vicki
I have found a Crawford family with a Claughton connection but I can't connect your James Francis Crawford to the family. Both the 1851 & 1861 census have an Amy Theresa Crawford born in Claughton, Cheshire
1851 Census West Kirby, Cheshire
HO107; Piece: 2174; Folio: 131; Page: 13
Eliza Crawford wife married 43 Born Dublin Ireland
Fanny Crawford daugh 19 born Liverpool, Lancashire
Eliza Margret daugh 4 born Liverpool, Lancashire
Amy Theresa Crawford daugh 1 born Claughton, Cheshire
1861 Census West Kirby, Cheshire
RG 9; Piece: 2638; Folio: 57; Page: 15
Eliza Crawford head married 52 born Ireland
Lilley Crawford daugh 14 born Liverpool, Lancashire
Amy Theresa Crawford daugh 11 born Claughton, Cheshire
Both censuses have Eliza as married but no husband at home.
Eliza Margret & Lilley could be the same person with Lilley a pet name?
This looks like the family in 1841 census
1841 Census Chester St, Toxteth Park (Liverpool)
HO107; Piece: 567; Book: 7 Folio: 6; Page: 5
James Crawford 35 Broker
Eliza Crawford 30
Frances Crawford 6
George Crawford 4
Frances Eliza Crawford of West Kirby married George Russell Alexander 9th June 1857 St Brides Church, Liverpool, the father of the bride was James Crawford, merchant.
The 1871 Scottish census has Eliza and Amy Crawford with the Alexander family in Partick, Scotland
1871 Scottish Census 11 Gardener Ter Cecil St, Partick, Lanarkshire
Goerge R Alexander head 50 born Edinburgh, Midlothian
Frances C Alexander wife 39 born Liverpool, Lancashire
6 Alexander children
Elizabeth Crawford mother-in-law 63 born Dublin, Ireland
Amy Crawford sister-in-law 21 born Birkenhead, Cheshire
James Crawford being a broker/merchant could explain why he wasn't at home for the 1851 and 1861 census.
Andy