First, toast the coconut. Turn broiler on to 400F. Line a baking pan with foil, and spread shredded coconut out in a single layer. Place in oven and toast, stirring often, until golden brown. Let cool slightly, then using a food processor, pulse until it's as fine as it will get. Set aside.
Preheat oven to 350F. Spray a bundt pan with baking spray {the type with flour in it}, or butter and flour by hand. Set aside.
In a medium bowl, mix together flour, pudding mix, toasted coconut, baking powder, baking soda, and salt.
In the bowl of a stand mixer, beat together the butter, coconut oil, and sugar until light and fluffy (2-3 min). Add in the vegetable oil, coconut extract, and rum. Add in the eggs, one at a time, beating until well combined.
Finally, add in the flour and mix until dough forms. Pour into prepared bundt pan.
Bake for 55-60 minutes until cake tester comes out clean. Let cool slightly then invert onto serving platter. Next, make the glaze.
In a small saucepan combine butter, sugar, and rum over medium heat just until sugar dissolves and glaze is smooth. If you cook it too long, the rum will evaporate out.
Using a pastry brush {or spoon}, soak the cake with the glaze. Serve and enjoy!