Preheat oven to 350 degrees F (175 degrees C). Grease a 9x5-inch loaf pan.
Mix flour, 1 1/4 cup white sugar, brown sugar, baking soda, cinnamon, baking powder, and salt in a large bowl. Stir mashed banana, canola oil, pineapple, flaked coconut, 1/4 cup walnuts, 1/4 cup macadamia nuts, eggs, applesauce, vanilla extract, lemon extract, and coconut extract into flour mixture until blended. Pour batter into prepared loaf pan.
Bake in the preheated oven until a toothpick inserted in the center of the loaf comes out clean, 70 to 80 minutes. Cool bread in the pan for 10 minutes; remove and transfer to a wire rack to cool, 20 to 30 minutes.
Mix butter, 1/4 cup white sugar, 1/4 cup walnuts, 1/4 cup macadamia nuts, and milk together in a bowl. Spread on top of bread once it has been transferred to the wire rack.