In the 1851 Onchan census mentioned by Len, 3 year old Reuben Hastings Palmer has an older brother Francis K Palmer age 12.
In 1861, there's a 22 year old Francis Kent Palmer, draper, boarder in Everton district 22 page 16, born Tipperary.
You say that Reuben Elliot Palmer had a son called Francis Kent Palmer. Did he name his son after his older brother. Does this suggest that Reuben Elliot and Reuben Hastings are the same person ?
In 1851 Reuben Hastings Palmer has a sister Anna Maria Palmer age 4, born Onchan.
Family search has this-----
ANN MARIA PALMER Pedigree
Female
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Event(s):
Birth:
Christening: 15 NOV 1846 Onchan, Isle Of Man, England
Death:
Burial:
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Parents:
Father: JOSEPH PALMER Family
Mother: SARAH
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Messages:
Extracted birth or christening record for the locality listed in the record. The source records are usually arranged chronologically by the birth or christening date.
------which corresponds with the names of Reuben's parents in the 1851 census.
Hope this helps
Jean C