The first Carter married a Catherine McGrath, before arrival in St. Peter's. I do know that the first Carter was actually named Snell, and changed his name to Carter on arrival in Cape Breton. The children of this couple were born very early 1800s. I do not know the origins of Snell/Carter and McGrath wife, other than the fact they were both born Nova Scotia. Does this meet with the info you have?
Halifax, Nova Scotia