That's very kind of you Mary.
If you get a chance at the MM there are some baptisms of the children Alan is sure are the right family, and they might have extra details to help identify which Thomas Cottier was their father (especially the last two who were born in New York, according to censuses). Thomas appears to have died in NY because Mary was a widow in the 1851 census. Thomas probably went to NY in 1836, and he was alive in the possible 1840 NY census entry. Mary and children were back in the IOM for the children's bapts in 1845. Was the father given as deceased?

[Parents Thomas Cottier and Mary Lawson.]
CATHERINE LAWSON COTTIER bapt 1 JUN 1834 Saint Mathews, Douglas, buried 1836.
MARY ANN COTTIER bapt 1 JAN 1836 Saint Barnabas, Douglas - not found later.
MARTHA MATILDA COTTIER Birth: 28 MAY 1839; Christening: 12 FEB 1845 Ballaugh.
THOMAS LAWSON COTTIER Birth: 20 DEC 1841; Christening: 12 FEB 1845 Ballaugh.

Thanks.
Sue