Combine marinade mix and orange juice in a resealable bag. Add pork, turning to coat. Marinate in the refrigerator for 30 minutes.
Remove pork from marinade; discard marinade. Grill pork over direct medium heat for about 20 to 25 minutes, turning occasionally, until internal temperature is at least 150°F.
Remove to cutting board and allow to rest at least 10 minutes. Cut into thin slices.
To assemble Cuban sandwiches, spread mustard over bottom half of each kaiser roll. Top with ham, sliced pork, dill pickle slices, Swiss cheese and top half of bun.
Cook in panini maker or in a nonstick skillet over medium-high heat for 3 to 4 minutes, just until cheese is melted.