Bring eggs, 1 1/2 teaspoon salt, and 1 quart water to boil in medium saucepan. Remove pan from heat, cover a let sit for 10 minutes. Transfer eggs to bowl filled with ice water and let cool for 5 minutes, then peel and chop coarse.
Place potatoes in large saucepan with cold water to cover by 1 inch, Bring to boil over high heat, add 1 teaspoon salt, reduce heat to medium-low, and simmer until potatoes are tender,15 minutes.
Drain potatoes , then spread out on rimmed baking sheet. Mix 2 Tablespoons pickle juice and mustard together in small bowl,, drizzle pickle juice mixture over hot potatoes, and toss until evenly coated. Refrigerate until cooled, about 30 minutes.
Mix remaining ingredients in cooled potatoes. Toss in cooled potatoes, cover, and refrigerate until well chilled, gently stir in eggs, just before serving.