Line an 8" x 8" square pan with aluminum foil; grease foil with butter.
Combine first 3 ingredients in a large heavy saucepan over medium heat. Bring to a boil; boil 8 minutes, stirring constantly. Remove from heat. Add marshmallows and remaining 3 ingredients to milk mixture; stir until marshmallows and morsels are melted and mixture is smooth. Pour fudge into prepared pan. Cool completely. Cut into 1" squares.
Note: If you can't find Key lime juice, use the same amount of fresh squeezed lime juice. The fudge will be slightly sweeter and less tart.