Ewan, are you thinking that Alice E Bowers might be the Alice who was living with William H Cox in 1901 in Douglas ?
I can't find a credible Alice E Bower/Bowers in 1901. Looking back at Alice and Edith in earlier censuses, it turns out that their parents were George Thomas Bowers and Sarah Rogerson. In 1871, Alice was 9, and in 1881 she was 19.
This is her baptism:
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England & Wales Christening Records, 1530-1906
about Alice Elisabeth Bower
Name: Alice Elisabeth Bower
Gender: Female
Birth Date: abt 1862
Christening Date: 21 Jan 1862
Christening Place: Stockport, Cheshire, England
Father's Name: George Bower
Mother's Name: Sarah
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and Edith:
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England & Wales Christening Records, 1530-1906
about Edith Sara Bowers
Name: Edith Sara Bowers
Gender: Female
Birth Date: abt 1873
Christening Date: 11 May 1873
Christening Place: Stockport, Cheshire, England
Father's Name: George Thomas Bowers
Mother's Name: Sarah Rogerson
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So an age of 40 in 1901, if she were Alice "Cox", would be about right for someone claiming to be the wife of a 60 yr old.
I've just read your 11 Feb update in which you refer to "Alice Emily ?" --- so if Emily was definitely her middle name, then this rules out Alice E Bowers.
This is AEB in the censuses (Ancestry's transcriptions):
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1871
Lancashire, Heaton Norris, Heaton Norris, 4/12
2 Church Terrace
Name Age
George S Bower 39
Sarah R Bower 41
Charles Bower 2
Alice E Bower 9
Margaret Bower 6
Kate C Bower 4
Mary Bates 26
George T Bower is a corn factor b Stockport
Sarah + Charles b Heaton Norris
others b Stockport
Mary Bates serv
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1881
Lancashire, Heaton Norris, 6/31
12a Lloyd St
Name Age
Sarah R. Bowers 52
Alice E. Bowers 19
Margaret Bowers 16
Edith A. Bowers 7
George R. Tyndall 24
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Hope this helps
Jean C