1 1/2 pounds fingerling potatoes (such as La Ratte or Russian Banana), cut into 1/2-inch disks
1/2 pound yukon gold potatoes (about 1 large), peeled, quartered lengthwise, and cut into 1/2-inch slices
Kosher salt
2 1/2 tablespoons white wine vinegar, divided
1 tablespoon whole grain mustard
1 tablespoon pickle relish
1 tablespoon sugar, plus more as desired
2 small shallots, one minced (about 1/4 cup), one thinly sliced (about 1/4 cup)
1/4 cup extra-virgin olive oil, divided
1 tablespoon capers, rinsed, drained, and roughly chopped
2 stalks celery, finely diced
1/4 cup roughly chopped fresh parsley leaves