Set to 350°F and line pans.
Whisk flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
Combine sugars, oil, applesauce, and milk.
Mix wet and dry ingredients, then add carrots, pineapple, and coconut.
Divide into pans; bake 30–35 minutes.
Cool 15 minutes, then transfer to rack.
Beat cream cheese, butter, sugar, vanilla, and juice.
Frost layers and garnish.
