For filling, in a bowl, combine sugar and tapioca. Add the raspberries, cherries (drained) and lemon juice; toss to coat. Let stand for 15 minutes.
Meanwhile, in a bowl, combine the flour, sugar, salt and baking powder; cut in shortening until crumbly. Combine the egg, water and vinegar. Gradually add to flour mixture, tossing with a fork until dough forms a ball.
Divide the dough in half. On a lightly floured surface, roll out one portion to fit a 9-inch pie plate. Place pastry in plate, trim even with edge.
Spoon filling into pastry. Dot with butter. Roll out remaining pastry to fit top of pie; make decorative cutouts from scraps, if desired. Place top crust over filling. Trim, seal and flute edges.
Cut slits in pastry. Brush cutouts with water; place on top of pie. Cover edges loosely with foil. Bake at 350 degrees F for 60-70 minutes or until golden brown.
Cool on a wire rack. Store in refrigerator.