To make the crust, sift the flour, baking soda, sugar, and cinnamon into a medium-size mixing bowl. Add the oil, yogurt, and vinegar and stir gently just until combined. Press the dough into a ball and divide in 1/2. Flatten each piece into a disk, wrap in waxed paper and refrigerate for 1 hour.

To make the filling, put the raisins in a medium-size bowl and pierce them with a fork so they will soak up the rum flavoring. Add the water and rum extract and stir to combine. Let stand at least 1 hour. Drain and return raisins to the bowl. In a saucepan, combine apple juice, apples, lemon juice, light brown sugar, granulated sugar, flour, cinnamon, and nutmeg. Cook over medium heat until the mixture has thickened, about 3 minutes. Add raisins and remove from the heat.

Preheat the oven to 425 degrees F.

On a lightly floured surface, roll out 1 piece of dough and fit it into a 9-inch pie plate. Add the filling. Roll out the remaining dough, fit it over the top of the pie, pinching the edges together to seal. Trim and crimp the edges. Pierce the top of the pie in a few places with a fork to make steam vents.

Bake for 10 minutes at 425 degrees F. then reduce the oven to 325 degrees F. and bake until apples are tender and crust is browned, about 45 minutes. Place on a rack to cool. Cut into wedges and serve.