Roy,
It is possible that both marriages for Cornelius are the same man but the one in 1728 is simply a different Mary White....not the same Mary White who was the widow of Peregrine White. I had gotten that from a write up regarding Judevine history but it's likely that was in error.
You show a baptism for William in 1738. Wouldn't this imply that his mother was Jane Rogers? It would then make sense why he would name a daughter Jane Rogers Judevine.
On Ancestry I find a baptism for a Cornelius Judevine (25 Jun 1710) at St. Lawrence in Thanet, Kent, England with his parents listed as Cornelius and Susanna. I have wondered if this is a possibility as there was a Huguenot community there.
http://search.ancestry.com/cgi-bin/sse.dll?indiv=1&db=FS...