OP is basically concerned with entry into SXM and Anguilla. A US passport is valid for entry into the US up to midnight of the expiry date of the passport and according to the US agency site entry into SXM and Anguilla will not be a problem for the time they wish to visit.

Bringing a copy of the agency information along just in case the airline is not up to speed on the regulations is a good idea.

French West Indies (not including St. Martin when entering from Dutch side) is 6 months as Carol mentioned.