1. Preheat the oven to 350 degrees. Spray 2 8-inch baking pans with baking spray or grease and lightly flour.
2. In the bowl of your stand mixer, combine the white cake mix, eggs, milk, sour cream, applesauce, key lime juice and key lime zest and mix on low speed until fully combined.
3. Divide the batter in half and pour each half into the prepared baking pan. Smooth the batter on top and tap the pan on the counter to remove any bubbles.
4. Bake the cake for 25-28 minutes or until lightly golden and a toothpick inserted in the center comes out clean.
5. Transfer the cakes to a wire cooling rack to allow to cool.
6. Prepare the glaze by adding the butter to a small saucepan over medium heat and melting. Whisk in the sugar and key lime juice, whisking until the sugar dissolves. Remove from the heat and whisk in the coconut rum.
7. Prick holes into the cake with a fork or toothpick and pour the glaze on top, allowing it to soak down into the cake. Let cakes soak for 10 minutes.
8. Run a butter knife around the edge of the cake and invert over a plate. Repeat with the second cake. Cut off the top layer of the cake to make it even, if necessary.
9. Prepare the frosting by combining the softened butter and shortening together in the bowl of a stand mixer and beating on medium high speed until light and fluffy. Add the coconut extract and coconut rum. Slowly add in the powdered sugar ½ cup at a time, alternating with the coconut cream until both are used and a thick frosting has formed.
10. Spread a heaping layer of the frosting on top of one of the cooled cakes. Carefully lift up the other cake and place on top. Add more frosting to the top of the cake, leaving the sides naked. Sprinkle shredded coconut on top and then arrange lime slices on the frosting.
11. Slice and serve immediately or store in the refrigerator until ready to serve.