I don't see any mention of the 1871 census entry in the earlier messages (or have I missed it ?)
Since in 1881 (at 6 Athol Sq) widow Selina has got John 25 lath splitter b Lpool, George 18 and Catherine 14 both b Douglas, (and 21 yr old Rebecca at 26 Atholl St as a dom serv to a retired surgeon ? ), I think this is the family 10 years earlier, showing that William b 1827 was still alive:
1871
Braddan F 4b/12+13
1 Atholl Sq
Ancestry's transcription
1871 Isle of Man Census
about Rebecca Cain
Name: Rebecca Cain
Age in 1871: 10
Estimated birth year: abt 1861
Relation: Daughter
Father's name: William Cain
Mother's name: Jemmia Cain
Gender: Female
Where born: Douglas, Isle of Man, Isle of Man
Civil Parish: Braddan
Town: Douglas
County/Island: Isle of Man
Country: Isle of Man
Street address: View image
Condition as to marriage: View image
Occupation: View image
Disability: View image
Registration district: Isle Of Man
Sub-registration district: F
ED, institution, or vessel: 4b
Neighbors: View others on page
Household schedule number: 312
Household Members: Name Age
William Cain 43
Jemmia Cain 45
John Cain 15
George Cain 8
Rebecca Cain 10
Catherine Cain 4
Wm lath splitter b Douglas
John lath splitter b Lpool
Perhaps the census taker scribbled down Selina, and then couldn't read his own handwriting, so guessed Jemmia.
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Since William gives his age as being 2 years less than Selina in the censuses, and since Selina was baptised April 1825, I looked at baptisms for Wm Cain in 1827/8 in Douglas.
I think that Philip Cain (innkeeper) and Mary Young were likely to have been the parents of Selina's husband, William Cain b 1827, as suggested by your friend, Jackie. The 19 May 1825 Braddan marriage gives Mary's surname as Younghusband (a mistranscription ?)
1841
Onchan 3a/12
Queen St
Philip Cain 40 publican Y
Mary 40 E
John 15 Y
William 14 Y
Philip 12 Y
Jane 11 Y
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1851
Conchan 3b/26 (next page to Wm+Selina, adjacent entry but different road name)
Queen St
Saddle Inn
1851 Isle of Man Census
about Phelip Cain
Name: Phelip Cain
Age: 53
Estimated birth year: abt 1798
Where born: Braddan, Isle of Man, Isle of Man
Relation: Head
Gender: Male
Civil Parish or Township: Conchan
Town: Douglas
County/Island: Isle of Man
Country: Isle of Man
Street address: View image
Condition as to marriage: View image
Occupation: View image
Disability: View image
Registration district: Isle of Man
ED, institution, or vessel: 3b
Neighbors: View others on page
Household schedule number: 115
Household Members: Name Age
Phelip Cain 53
Jane Cain 24
Robert Cain 9
Sarah Cain 6
Mary Ferguson 30
Margaret Pelly 38
William Johnson 19
James Swmbarne 31
Philip wid b Braddan
children Jane, Robt + Sarah b Douglas
others are servants
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Children of Philip Cain and Mary Young from IGI:
1. WILLM CAIN - International Genealogical Index
Gender: Male Christening: 08 JUL 1827 Saint George, Douglas, Isle Of Man, England
2. PHILIP CAIN - International Genealogical Index
Gender: Male Christening: 23 NOV 1828 Saint George, Douglas, Isle Of Man, England
3. JOHN CAIN - International Genealogical Index
Gender: Male Birth: 01 JAN 1826
4. JOHN CAIN - International Genealogical Index
Gender: Male Christening: 08 JUL 1827 Saint George, Douglas, Isle Of Man, England
5. JANE CHRISTIAN CAIN - International Genealogical Index
Gender: Female Christening: 04 APR 1830 Saint George, Douglas, Isle Of Man, England
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Robert and Sarah were't listed, so I speculated that Mary nee Young had died, and Philip had remarried. There's a 27 Jan 1842 marriage in Braddan of Philip Cain to Sarah Creer (nee Dickinson ?)
children of Philip Cain and "Sarah Dickinson or Creer":
1. SARAH MARGT CAIN - International Genealogical Index
Gender: Female Christening: 19 MAY 1844 Saint Mathews, Douglas, Isle Of Man, England
2. ROBERT DICKENSON CAIN - International Genealogical Index
Gender: Male Christening: 05 OCT 1842 Saint George, Douglas, Isle Of Man, England
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By 1851, Philip was a widower, so he may have buried 2 wives between 1841 and 1851
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perhaps the burial of Mary Cain nee Young ?
CAIN, Mary 41 Braddan 6 Oct 1841
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perhaps the burial of Sarah Cain nee Dickenson:
CAIN, Sarah 43 Braddan 31 May 1850
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Donna, please would you see if there are MIs or additional information in the burial indexes ?
I think that Wm and Selina's 1851 census entry being adjacent to that of Philip and Mary is a strong clue in linking them. What do you think ?
Jean C