I can't see any reason to move your search for Ann Cheyne to Ireland, just because someone of the same surname was in the IOM for a while and went to Dublin. In her 1828 marriage she was from Banff, Scotland: "William Bremner in the Parish of Fordyce and Ann Cheyne in this Parish".
It is still possible that the family lived in Peel for a while, and their son was born there - his bapt didn't say where born, only that it was about a month earlier than the baptism.

The IGI (at Familysearch.org. See "Search records" then choose International Genealogical Index in the left column) has five Ann Cheyne bapts in Banff between 1781 and 1812 (husband William aged 60 - rounded age - in 1841, according to Ancestry).

Did you look up the 1841 census on ScotlandsPeople? See my message of 31 January 2010 with the index for this (bottom of thread). The actual scan will give more accurate information. In particular, was aged 20 really the age given for the Ann there? Then 1851 would give ages and places of birth if we can find any of the family in that census.

Sue