In a large saucepan with a cover, mix the sugar, water, corn syrup, and vinegar. Stir until the sugar dissolves, then cover and cook for 3 minutes to melt any sugar crystals that may be on the sides of the saucepan. Remove the lid and continue cooking for about 12 minutes, until the mixture reaches the hard ball stage, about 265°F on a candy thermometer. The syrup will spin a long thread when poured from the edge of a spoon. Remove the syrup from the heat and stir in the marshmallows. The mixture will be foamy. With the mixer running at high speed, stream the syrup into the egg whites, following the groove the beaters make as the bowl turns. Beat well and add the vanilla.