Preheat the oven to 350 degrees F. Lightly coat a 9X13-inch pan with cooking spray. Set aside.
In a medium bowl, whisk together the flour, cocoa, baking powder and salt. In a liquid measure or other bowl, whisk the buttermilk, red coloring and vanilla together.
In a large bowl, using an electric mixer on medium speed, beat sour cream, oil, butter and sugar until fluffy, about 3 minutes. Beat in eggs one at a time, scraping down sides of bowl. Add half of flour mixture and mix. Add the buttermilk/food coloring mixture and mix again, scraping down the sides of the bowl as needed. Mix in the remaining flour until just combined. In a small bowl, mix vinegar and baking soda until mixture fizzes then quickly fold into batter. Scrape the batter into the prepared pan and tap on the countertop to burst any air bubbles. Bake until a toothpick inserted in center of cake comes out clean, 30 to 35 minutes. Don't overbake or the cake will be dry. Set on a wire rack to cool completely.
For the frosting, using an electric mixer on medium-high speed, beat together cream cheese, yogurt, butter and vanilla until well combined and smooth. Slowly mix in powdered sugar. When the cake is completely cooled, spread the frosting over the cake, cut into pieces and serve. If not serving right away, store the cake in the refrigerator until ready to eat. Alternately, you can spread the frosting on each individual piece instead of the entire cake.