Prepare crust: Using 2 pastry blenders, blend the flours, sugar, shortening, butter and salt. Whisk the egg, vinegar and water in a 2-cup measure and pour over the dry ingredients incorporating all the liquid without overworking the dough. Dust additional flour over the ball of dough and chill if possible. Divide the dough in two. Roll out 1 piece of dough to make a bottom crust. Place into a pie dish. Put dish in refrigerator to chill.
Preheat oven to 425 degrees F.
Prepare Filling: Mix the rhubarb, strawberries, sugar, tapioca, flour, zest and juice of lemon, dash of cinnamon, and vanilla. Mix well in a large bowl and pour out into chilled crust. Dot the top of the filling with the butter. Brush edges of pie crust with egg white wash.
Roll out the other piece of dough and place over filling. Crimp to seal edges. Brush with egg white wash and garnish with granulated sugar. Bake at 425 degrees F for 15 minutes. Decrease temperature to 375 degrees F and bake for an additional 45 to 50 minutes, or until the filling starts bubbling. Higher altitude will take 450 degrees F and 400 degrees F respectively.