In a food processor, pulse the flour, sugar and salt. Add the butter and shortening and pulse until a course crumbly texture forms. Add the apple cider vinegar/cold water mixture 1 tablespoon at a time until you reach the desired consistency. Pinch the dough between your fingers and if it doesn't stick together, add 1 tablespoon of ice water at a time, pulsing between additions until the dough comes together. Do not overmix or the dough will become tough.
Divide the dough between 2 sheets of plastic wrap and pat each into a disk. Wrap tightly and refrigerate until firm, at least 1 hour or preferably overnight, or freeze for up to 2 months. Roll out the dough and use as desired.