For the Kids (Serves 2): In a small bowl, combine ketchup and mayonnaise; set sauce aside. In a shallow dish, combine flour with a pinch of salt. In another dish, whisk together egg, 1 tablespoon water, and a pinch of salt. In a third dish, stir together breadcrumbs, 1/2 teaspoon salt, and 1/4 teaspoon pepper.
Working with one at a time, dredge cutlets in the flour to coat completely, then shake off excess flour. Dip the floured chicken in the egg mixture, turning to coat completely. Let excess drip off. Place cutlet in the breadcrumb mixture, patting it in and turning to coat both sides. Shake off any excess crumbs before proceeding.
In a large nonstick skillet, heat 2 tablespoons oil over medium; swirl to coat. Add 4 cutlets; cook until golden brown and no longer pink in the center, 2 to 3 minutes per side. Remove. Repeat with remaining oil and chicken. Cut half the cutlets into strips; serve with sauce.
For the Adults (Serves 2): Serve remaining cutlets with Olive Relish.