Preheat oven to 350°.
Put the dried fruit in a bowl and cover with 1/2 cup boiling water. Let it stand while you work on the rest of the batter.
Lightly grease 2 8-inch loaf pans and then dust with a bit of flour.
Beat the egg whites and egg in a medium bowl, and then add the applesauce, yogurt, oil, vanilla and rum. Once combined, whisk in the sugar, making sure its fully dissolved.
In a large bowl, whisk together the flours, baking powder, baking soda, salt, lime zest and coconut.
Add in the egg/yogurt/applesauce mixture to the dry ingredients. Then drain the dried fruit (discard the liquid), and fold the dried fruit into the batter.
Divide batter between the two pans. Bake at 350° for about 55-60 minutes or until a wooden pick inserted in center comes out clean. Cool in pans for 15 minutes on a wire rack.
8.Meanwhile, prepare the glaze. Whisk the powdered sugar with the lime juice and heat in the microwave for 30 seconds or so to help dissolve any lumps.
Remove the loafs from pans and transfer to a wire rack. Drizzle the glaze (you can use as much or as little as you like, but just know that it does add sweetness and tart flavour). Allow to cool completely before cutting in and eating.