Preheat oven to 325°F (163°C).
In a large bowl, beat the butter and shortening with an electric mixer until creamy.
Gradually add the sugar, beating at medium speed until light and fluffy.
Add the eggs, one at a time, beating just until blended after each addition.
In a separate bowl, mix together the flour, baking powder, and salt.
Add some of the flour mixture to the butter mixture, alternating with the milk. Begin and end with the flour mixture, beating at low speed just until blended after each addition.
Stir in the vanilla extract, lime zest, and key lime juice.
Pour the batter into a greased and floured 10-inch (12-cup) tube or Bundt pan.
Bake for 1 hour and 15 minutes to 1 hour and 20 minutes or until a long wooden pick inserted in the center comes out clean.
Cool the cake in the pan on a wire rack for 10-15 minutes.
In a small bowl, mix together the powdered sugar, key lime juice, and vanilla extract to make the glaze.
Remove the cake from the pan and brush the glaze over the top and sides of the cake.
Cool the cake completely, about 1 hour.