Preheat the oven to 425°F.
In a large mixing bowl, combine the cherries, rhubarb, sugar, flour, salt, vanilla extract, and lemon juice. Toss until the fruit is evenly coated. Let the mixture sit for about 10 minutes to allow the juices to develop.
Roll out one pie crust and fit it into a 9-inch pie pan.
Pour the cherry-rhubarb filling into the crust, spreading it evenly. Dot the filling with small pieces of butter.
Roll out the second pie crust and place it over the filling. Trim and crimp the edges to seal. Cut a few slits in the top crust to allow steam to escape.
Brush the top crust with the beaten egg and sprinkle with coarse sugar.
Bake in the preheated oven for 15 minutes.
Reduce the temperature to 350°F and continue baking for an additional 30-35 minutes, or until the filling is bubbly and the crust is golden brown. If the edges brown too quickly, cover them with foil.
Remove the pie from the oven and let it cool for at least 2 hours before serving to allow the filling to set.