In a medium bowl, whisk together the mustard, apple juice, vinegar, 2 tablespoons water, 1/4 teaspoon of the pepper, and 1/2 cup of the oil. Transfer 1/2 cup of the mixture to a large resealable plastic bag and refrigerate the rest. Pat the chicken dry with paper towels. Add to the bag, seal, and refrigerate for 20 minutes.
Meanwhile, heat grill to medium. Place the zucchini, tomatoes, and onion on a baking sheet. Add the salt and the remaining oil and pepper and toss.
Grill the chicken and vegetables, turning occasionally, for about 10 minutes total. Transfer to a cutting board and roughly chop the ingredients.
Divide the salad greens among individual bowls and top with the chicken, vegetables, and the reserved dressing.