1851 Jemima seems to be with other family Samuel & Mary Ann Hinde. She is described as sister in law, but could be sister in law to either of them. No Edward in sight though.
1861 - Town Street, Keyworth
(she seems to be gaining years on the census!)
Edward Smedley aged 37, born Wysall, occupation Common Carrier
Jemima Smedley aged 37, born Keyworth, occupation Glove Seamer
Martha Smedley aged 11, born Keyworth, occupation Glove Stitcher
Henry Smedley aged 8, born Keyworth
Edwin Smedley aged 5, born Wysall
William Smedley aged 1, born Wysall
1871 -
(age slightly different again and husband and wife have swapped around their birth places)
Edward Smedley aged 47
Jemima Smedley aged 43
Edwin Smedley aged 13
William Smedley aged 11
Mary Smedley aged 8, born Keyworth
Ruth (S)Medley aged 5, born Lockington, Leics
Alice Smedley aged 2, born Lockington, Leics
John Smedley aged 4months, born Lockington, Leics
The Alice in 1871 is just on the birth index as Alice, not Lucy Alice and was just christened Alice on 11 October 1868 in Lockington.
Just looked at the 1881, where Edward is there (not widowed but Jemima is missing) and Alice is 12 and has been badly transcribed as Lucy. Its definitely Alice and not Lucy (not convinced it looks anything like Lucy).
They all disappear off the face so far in 1891. Do you know when Alice married?