Here is 1881 Dalton In Furness, Lancashire, England census for a William Hy & Emily Cain. The family was living in England and not the IOM when Elizabeth Ann Cain(e) was christened in Sept. 1882 in Barrow (Barrow In Furness?) Lancashire, England.

I've, also, included after the census, the birth records for the two children listed in the 1881 UK Census.
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Household::

Cain, William Hy.-head-M-male-age 23, born Patrick, IOM-Iron Ore Miner
Cain, Emily-wife-M-female-age 19, born Patrick, IOM
Cain, William F-son-male-age 2, born Patrick, IOM
Cain, Emily Minerva Alice-Daug-female, born Patrick, IOM
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Dwelling: 93 New Cleator St.
Census Place: Dalton In Furness, Lancashire, England
Family History Library Film: 1342023
Public Records Office Reference: RG11
Piece/Folio: 4282/25
Page Number: 23
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Name: William Freddy Cain
Gender: Male
Birth Date: 30 Sep 1878
Birthplace: Peel, Isle of Man, England
Father's Name: William Cain
Father's Birthplace:
Mother's Name: Emily Kelly Cain
Indexing Project (Batch) Number: C00829-6
System Origin: Isle_Of_Man-ODM
Source Film Number: 454963
Reference Number:
Collection: Isle of Man Births and Baptisms, 1821-1911
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Name: Emily Minerva Alice Cain
Gender: Female:
Birth Date: 01 Apr 1880
Birthplace: Peel, Isle of Man:
Father's Name: William Cain
Mother's Name: Emily Kelly Cain
Indexing Project (Batch) Number: C00829-6
System Origin: Isle of Man-EASy
Source Film Number: 454963
Reference Number: Vol 1 Pg.108 No. 133
Collection: Isle of Man Births and Baptisms, 1821-1911
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