Preheat oven to 350 degrees F. Generously coat a 9- x 5-inch loaf pan with nonstick cooking spray.
Using a handheld or stand hand mixer, beat together 2 tablespoons of softened butter and cream cheese in a large bowl until fluffy. Add the white sugar and beat until well incorporated. Add the egg and mix well.
In a separate mixing bowl, combine the flour, baking powder, baking soda, and salt. In a different bowl combine the mashed bananas, milk, 2 tablespoons rum, lime zest, lime juice, and vanilla extract.
Using a wooden spoon, alternate mixing the flour mixture and banana mixture into the creamed butter mixture, in increments, until both have all been added and it is well combined. Fold in ¼ cup pecans and ¼ cup coconut. Pour the mixture into the prepared loaf pan.
Bake in the preheated oven for 55 to 60 minutes, until toothpick inserted in center of loaf comes out clean. Remove from oven and allow to cool for 5 to 10 minutes in the pan, then remove from the pan and transfer loaf to a wire rack to continue cooling.
Meanwhile, prepare the glaze. Place the brown sugar, butter, lime juice and rum in a small saucepan over MEDIUM heat. Bring to a low boil stirring constantly. Cook, stirring, until the sugar has dissolved and the mixture is smooth, about one minute. Remove from heat and stir in 2 tablespoons pecans and 2 tablespoons coconut. Let the glaze rest for two minutes and then spoon it over the loaf while it is still slightly warm. The glaze will set up as the loaf cools.