Your best bet is to obtain a copy of Jack Corkill's birth certificate which may give his father's name and occupation.
He and his parents may also be in the 1930 US census to which I do not have access. His parents and siblings may be in the 1900 US census to which I do not have access.
Do not forget to check John and Corkhill as well.
The one pair on twin sisters I did find in Brian Lawsons births index are Ada Mary and Christian Corkill born Apr 30 1895 to Henry Corkill and Isabella Ann Skillicorn in Ramsey. They had two siblings Henry Edward b. Jan 11 1893 and Elizabeth Ann b. Jan 5 1897. That would make Henry Edward a father at 15. This family does not appear in the 1901 IOM census, so they may have emigrated and you may want to check passanger and immigration records.