Hello, I am also a descendant of Peter Bertrand. My grandfather was John Austin Bertrand, whose father was Austin C. Bertand, whose father was John R. Bertrand, whose father was Pierre "Peter" Gabriel Bertrand. All of these men, except Peter Bertrand, are buried in the same cemetery near where my grandparents lived in central Texas.
I don't have any facts for you, but the lore I've heard differs slightly from what you've heard. I heard that Peter Bertrand left Haiti on a ship to the US, hiding in a bundle of sugar cane, while his mother and sisters went to Cuba and then to France. He lived in the east and south, and then eventually moved to Braziora County, then in Mexican Texas.