Eric,
Yes, David Quayle & Catherine Kelly are the parents of Phillip & Thomas.
I am in touch with Robert Quayle (U.S.A.) who is the gt.gt. grandson of Thomas Quayle, and he is in touch with Joseph Quayle in Australia who is a descendant of Daniel Quayle another son of Phillip & Margaret and a brother to Jane.
Robert has traced the Quayle family back to John Quayle who died in Kirk Michael 1711, wife was Bahee Cannell.
Guess there's a lot of Quayles out there!!