Put the potatoes in a 6-quart pot; add 2 Tbs. salt and enough water to cover by 1 inch. Put the scapes on the potatoes. Bring to a boil over high heat, then lower the heat to medium, and simmer vigorously until the scapes are just tender, about 5 minutes after the water boils. With tongs, transfer the scapes to a cutting board and cut into 1/2-inch pieces.
Continue to simmer the potatoes until just tender when pierced with a fork, about 15 minutes more. Add the peas and simmer until crisp-tender, 1 to 2 minutes. Drain the potatoes and peas in a colander. With tongs, transfer the potatoes to a cutting board. Rinse the peas under cold water to stop the cooking, and let drain. While the potatoes cool, whisk the mayonnaise, oil, lemon zest and juice, and 1/2 tsp. each salt and pepper in a small bowl. In a large bowl, mix the vinegar with 2 tsp. salt and stir to dissolve.
When the potatoes are just cool enough to handle, scrape their skins off with a paring knife and cut them into 3/4 to 1-inch pieces. Toss them in the vinegar-salt mixture, and then stir in about half of the dressing. Add the scapes, peas, scallions, herbs, the remaining dressing, and salt and pepper to taste and mix well. Let cool to room temperature before serving.