Mix the flour and solidified coconut oil together. Stir in the sugar, salt, and water. Knead the mixture into a smooth ball and refrigerate for 1 hour.
Peel and slice the apples, then stir in the rest of the listed ingredients until combined.
Heat a skillet over medium heat with some vegetable oil. Season the chicken breast and fry until golden brown. For extra tender chicken, pour some broth into the skillet, then cover and let simmer for 20 minutes, stirring occasionally. Remove from the heat and let the chicken cool, then use a fork to pull the meat apart. Next, heat the skillet with some vegetable oil and briefly fry the garlic and onion. Add the shredded chicken breast, carrots, mushrooms, peas, paprika, and chicken broth. Whisk together the milk and corn starch, then pour the mixture into the skillet with the other ingredients. Finally, stir in the cream cheese and shredded mozzarella and season with salt and pepper to taste.
Preheat the oven to 375°F. Using aluminum foil, divide the 11-inch pie dish into 2 distinct sections.
Halve the pie crust dough and roll out 1 half. Cut the rolled-out dough in half and place 1 dough half in each half of the pie dish. Spoon the apple pie filling into 1 half of the pie dish, and the chicken pot pie filling into the other half of the pie dish.
Roll out the second half of the pie crust dough and cut it in half. Use 1 of the halves to cover the chicken pot pie filling. Cut the other dough half into strips and weave them together to create a lattice top pattern. Carefully place the lattice top over the apple pie filling and trim the edges to get rid of any excess dough. Refrigerate the split decision pie for a few minutes to make sure the crust holds its shape.
Make a few incisions in the chicken pot pie crust to let steam escape while it's baking. Transfer the pie dish to the oven and bake at 375°F for 40 minutes.