Toss chicken with 2 teaspoons salt. Bring water and broth to a boil in a large saucepan, then add chicken and cook at a bare simmer, uncovered, stirring occasionally, until just cooked through, about 5 minutes. Drain and cool, then tear into 1-inch chunks.
Meanwhile, stir together yogurt, mayonnaise, and mustard.
Stir chicken and remaining ingredients into dressing with salt and pepper to taste.