Sprinkle a small amount of water on a large sheet of plastic wrap. Place 2 of the pork slices on top of the plastic and sprinkle again with water. Cover with another sheet of plastic wrap and pound with a rolling pin or meat pounder until about 1/4 inch thick. Repeat with the remaining pork.
Mix the flour with the salt and pepper in a shallow pie plate. Heat half the oil and butter in a large skillet over medium-high heat until almost smoking. Working in two batches, place the pork in the flour mixture and turn to coat on all sides. Shake off the excess flour and add to the skillet. Cook until lightly browned, about 2 to 3 minutes per side. Transfer to a plate or platter and cover loosely with foil. Repeat with the remaining butter, oil, and pork.
Return the skillet to the heat and add the grapes and onion. Reduce the heat to medium and cook, stirring often, until the onions are slightly softened, about 5 minutes. Increase the heat to high, pour in the wine, and bring to a boil. Cook rapidly, stirring to pick up any browned bits in the bottom of the skillet, until reduced to about 1 tablespoon. Add the broth and sugar and boil until reduced by half. Reduce the heat to medium and return the pork to the skillet with any accumulated juices. Simmer gently until heated through, 3 to 5 minutes. Transfer the pork to a large heated platter. Remove the skillet from the heat, whisk in the mustard, and season the sauce with salt and pepper. Pour the sauce over the pork and serve hot.