Preheat oven to 350 degrees Fahrenheit. Grease or paper-line 30 baking cups.
In a medium bowl combine the flour, baking soda, baking powder, and salt. In a separate mixing bowl, cream the butter and sugar. Beat in the eggs, one at a time. Add the vanilla, key lime juice and lime zest; mix well. Add the flour mixture to creamed mixture alternately with sour cream (batter will be thick). Fill muffin cups with 1/4 cup of batter. Bake at 350 degrees F for 20-25 minutes or until a toothpick inserted near the center comes out clean. Cool completely and frost as desired.
Place blackberries in a small bowl and sprinkle with sugar, let thaw. Drain blackberries, reserving liquid. Squish the blackberries and push through a fine mesh sieve to remove the seeds, set aside. Add enough water to the blackberry liquid to equal 1 cup. In a large saucepan, combine the blackberry liquid, lemon juice, cornstarch, and salt. Heat and stir until the mixture boils and thickens. Cool completely. Refrigerate until ready to use. (This can be made several days in advance and any leftovers works well on toast, on pancakes, or mixed in plain Greek Yogurt.).
Beat butter and vanilla until creamy. Mix in blackberry filling and salt. Add powdered sugar 1 cup at a time, beating until combined. Add milk 1 tablespoon at a time until you reach desired consistency.