Hello Sue, there is no mention of a Son named Peter in the following Will,

40.

This is Affirmed to be the Last Will and Testament __
of Peter Corkill of the parish of KK Braddan who Departed
this Life on the Sixteen of March 1771 – First He commit
= ed his Soul to God and his Body to Christian Burial __
He Appointed and Nominated Thos. Corkill of Ballaughtyn
to be his Whole and Sole Executor of all his Goods What =
= soever
Witnesses present

Elizabeth Oates my mk X }

Dorothy Christian my mk X } Jurati

At a Chapter Court holden near Douglas 21st Oct 1771

The Execr. Is Sworn in Court in form of Law & hath
given Pledges in form of Law Pledges for the
Payment of Debts & Legacies are Nicholas Quirk
& Wm. [Carralash]

Joh : Moore

Thos. Cubbon