An IOM marriage in 1834 is unlikely to give you the information you are looking for, unless she was underage (under 21), and her father or other relative was named as having given permission for the marriage.

In the 1851 census they were in Toxteth Park, Lancs, at 19 Bk Parliament St. They are all listed as born Isle of Man, but the parish was not given (you might find this in another census). William Cottier Head Mar, 35, Joiner (House), with wife Ann 36? The "6" has a break at the bottom. Children Jane 11, William 9, Ann 5.

Sue