I have ATT unlimited plan as well.
In St Thomas and Mexico , your phone will work just as if you were at home.
You will need an international plan for St Martin and Honduras (or find a WIFI hot spot and use WIFI calling) You can sign up for "International Day Pass" which will give you coverage in those countries. The nice thing about it is, if you are able to accomplish the WIFI calling, you won't be charged anything by ATT. You are only charged a $10 fee IF you connect to the cellular system in that country, if you don't connect, there is no charge.