My family from my mom's side is from Ponce, Puerto Rico, and they are Tricoche's as well. Our story is a bit different though, apparently, our great great great grandmother moved from France to Ponce and she had a child with a merchant from New Orleans. The baby carried his mother's last name, Tricoche, rather than Hamilton. I am not 100% sure how accurate this is but I am sure it will help to build your tree. I can help in as much as I can.