Combine the sugar and water in a small saucepan over medium; bring to a boil. Add rhubarb and 1 cup strawberries. Reduce heat and simmer, stirring often, until the fruit is tender, about 3 minutes. Pour the mixture through a wire-mesh strainer into a bowl; use the back of a spoon to squeeze out the juices. Discard the solids. Chill the syrup until cold, about 1 hour.
Combine the syrup, peaches, and the remaining 1 cup of strawberries in a 3-quart pitcher. Top with the chilled wine just before serving and garnish with mint.