Preheat oven to 325°. In a mixing bowl, whisk together flour, baking powder, and salt; set aside.
In the bowl of a stand mixer, beat butter and shortening at medium speed until creamy. Gradually add sugar, beating until light and fluffy. Add eggs, 1 at a time, beating just until blended.
Add flour mixture to butter mixture alternating with milk, beginning and ending with flour mixture. Beat at low speed just until blended after each addition.
Mix in vanilla, lime zest, and lime juice. Pour batter into a greased and floured 10-inch (12-cup) tube pan. (I used two 6-cup bundt pans.)
Bake for 1 hour and 15 minutes to 1 hour and 20 minutes or until a long wooden pick inserted in center comes out clean. (Bake half size Bundts for 50–55 minutes.) Cool in pan on a wire rack 10 to 15 minutes; remove from pan to wire rack.
Prepare Key Lime Glaze by whisking together powdered sugar, 3 tablespoons fresh Key lime juice, and ½ teaspoon vanilla until smooth. Immediately brush or drizzle over top and sides of cake. Cool completely before serving.