Preheat the oven to 300 degrees F (150 degrees C). Grease and flour a 10-inch tube pan; line with parchment paper.

Beat white sugar, butter, and shortening together with an electric mixer on medium speed until creamy.

Sift cake flour, baking powder, and salt together. Add flour mixture, eggs, and cream alternately to the butter mixture, beginning and ending with the flour mixture. Beat on low speed just until blended. Stir in Key lime juice, lime zest, and vanilla extract. Pour into the prepared pan.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 1 hour and 30 minutes. Cool in the pan on a wire rack for 15 minutes; remove cake from the pan to cool completely.

While cake cools, combine powdered sugar, Key lime juice, and vanilla extract in a bowl. Immediately brush glaze over the top and sides of the cake.