Hi - You need to get the marriage cert for Richard E Corrin and Margaret Hughes, presumably before your mother's birth in 1939 (Braaid, Marown).
This will give their fathers' names and occupations.
Buy certs from www.gov.im/registries/general/civilregistry/
See "Contacts" at the top of the screen.

See also www.manxbmd.com/marriages.html which shows scans of the indexes. The cert will cost less if you supply the index entry reference.

Sue