Alice must have survived, but was not with her family in 1851.
The 1844 death of Alice Longworth at London Road, Manchester, aged 0, was another, daughter of a Longworth & Sharples family.
Name: Alice Longworth Age: 8 Birth Date: abt 1844 Burial Date: 7 Oct 1852 Burial Place: Horwich, Holy Trinity, Lancashire, England Reference Number: GB127.L86/1/4/2
There is no Lancashire DMD record for Alice, although there is one listed for Catherine - perhaps a transcription error, recording the mother in error.
Lancashire Death indexes for the years: 1852 LONGWORTH Catherine 8 Horwich HOR/3/276
General Notes
Alice must have survived (as no death record), but was not with her family in 1851.