In a small microwave-safe bowl, combine cherries and apple juice. Cover and microwave on high until heated through; set aside.
In a small bowl, combine 2 tablespoons sugar and 1/4 teaspoon cinnamon; set aside for topping. In a large bowl, combine cornstarch with the remaining sugar and cinnamon. Stir in the apples, vanilla and reserved cherry mixture.
Line a 9-in. deep-dish pie plate with bottom crust; trim pastry even with edge of plate. Add filling. With remaining pastry, make a lattice crust. Seal and flute edges. Beat egg white until foamy; brush over lattice top. Sprinkle with reserved cinnamon-sugar.
Cover edges loosely with foil. Bake at 450° for 15 minutes. Reduce heat to 350° and remove foil. Bake 30-45 minutes longer or until crust is golden brown and filling is bubbly. Cool on a wire rack.