MAKE CURD: In a heavy saucepan whisk together yolks, sugar, butter, lemon, and lime juice. Cook over low heat, whisking constantly, until mixture just reaches a boil. Strain curd through a fine sieve into a bowl and stir in zest. Chill curd, its surface covered with plastic wrap, at least 4 hours.
PREHEAT oven to 350 degrees F. Line bottoms of three 9- by 2-inch buttered cake pans with parchment paper. Butter paper and flour pans, knocking out excess.
MAKE CAKE: In bowl whisk together flour, baking powder and salt. In a small bowl stir together milk, vanilla, and 3/4 cup coconut. In a large bowl with an electric mixer beat butter on medium speed 1 minute and gradually beat in sugar until light and fluffy, about 3 minutes. Beat in eggs, 1 at a time, beating well after each addition. Reduce speed to low and add flour mixture in batches alternately with milk mixture, beginning and ending with flour mixture and scraping bowl occasionally, until batter is just combined. Divide batter among pans and smooth tops.
BAKE layers in middle and lower thirds of oven until a tester inserted in center comes out clean, about 30 minutes. Cool
cake layers in pans on racks 10 minutes before turning out onto racks. Remove paper from cakes and cool completely.
PLACE 1 cake layer on a cake plate, dome side down, and spread evenly with about half of curd. Sprinkle with 1/4 cup coconut and chill 15 minutes. Repeat layering in same manner with another cake layer, remaining curd, and remaining 1/4 cup coconut and top with remaining cake layer, dome side up. Chill cake 15 minutes.
MAKE FROSTING: In top of a double boiler off heat with a hand-held electric mixer beat together all frosting ingredients except vanilla until combined. In double boiler (do not let bowl touch water) beat mixture on high 7 minutes, or until it holds stiff glossy peaks. (This may take longer in humid weather.) Remove from heat and add vanilla. Beat mixture
until cool, about 3 minutes. Spread frosting evenly over top and sides of cake and coat with coconut.