Preheat oven to 350 degrees F. Grease and flour a bundt pan.
In a saucepan over medium heat, combine brown sugar and 1/4 cup of butter. Bring to a boil, stirring often, then pour it evenly into the bottom of the bundt pan. Add the cranberries and mandarin oranges to the bottom of the pan over the brown sugar mixture.
In a large mixing bowl, cream together the remaining 1/4 cup butter, coconut oil, and sugar. Beat in the eggs, vanilla, yogurt and milk.
In a separate mixing bowl, combine the flours, baking powder, baking soda and salt. Stir the yogurt mixture into the flour mixture until batter is combined.
Pour the batter into bundt pan over the cranberry mandarin mixture. Bake it for 45-50 minutes until a toothpick inserted into the top comes out clean. Allow the cake to cool for 10 minutes, then quickly and carefully invert the cake over onto a serving plate.