Preheat oven to 375 degrees F (190 degrees C). Grease and flour two 9 inch round cake pans.
Make pudding according to package directions using the milk. Set aside 2 tablespoons of pudding and place the rest in the refrigerator. When chilled, pull the pudding out of the refrigerator, and stir in the pineapple.
In a large bowl, cream together the shortening and sugar, continue to mix with an electric mixer on medium speed for 15 minutes. Stir in the reserved 2 tablespoons of vanilla pudding. Beat in the eggs one at a time, mixing well after each addition.
In another bowl, sift together cake flour, baking powder, and salt. Add these dry ingredients to the creamed mixture alternately with 1 cup milk, blending well after each addition. Divide the batter evenly between the prepared pans.
Bake for approximately 20 to 25 minutes, or until the top springs back when lightly pressed. Set the pans on a wire rack to cool. Remove the layers from the pans.
Once the cake layers have thoroughly cooled, spread the pudding mixture on top of one of the layers (spread mixture to desired thickness - there may be some left over). Place the second layer on top of the filling. Frost the cake with the whipped topping. Refrigerate the cake until serving time.