Preheat the oven to 375°F. Line a 12-cup muffin pan with paper liners.
In a large mixing bowl, whisk together the flour, baking powder, baking soda, salt, and sugar.
In a separate bowl, whisk together the eggs, oil, coconut milk, sour cream, blended pineapple, pineapple juice, vanilla extract, coconut extract, rum extract, and lime zest until smooth.
Pour the wet ingredients into the dry ingredients and stir gently until just combined. Do not overmix.
Divide the batter evenly among the muffin cups, filling each about ¾ full.
Bake for 18–22 minutes, or until a toothpick inserted into the center comes out clean.
Cool in the pan for 5 minutes, then transfer the muffins to a wire rack to cool completely.
To make the glaze, whisk together the powdered sugar, coconut milk, and coconut extract until smooth.
Drizzle the glaze over the cooled muffins before serving.