For sauce, stir together rice wine, soy sauce, water, fish sauce (if desired), cornstarch, and crushed red pepper. Set aside.
Pour oil into a wok or large skillet. (If necessary, add more oil during cooking.) Heat over medium-high heat. Add ginger and garlic to wok; cook and stir for 15 seconds. Add carrots; cook and stir for 2 minutes. Add pea pods and green onions; cook and stir for 2 to 3 minutes more or until vegetables are crisp-tender. Remove vegetables from wok.
Add half of the chicken to hot wok. Cook and stir for 3 to 4 minutes or until chicken is no longer pink. Remove from wok. Repeat with remaining chicken. Return all chicken to wok. Push chicken from center of wok. Stir sauce; add to center of wok. Cook and stir until thickened and bubbly. Return vegetables to wok. Stir in the 1/3 cup peanuts. Cook and stir for 1 to 2 minutes more or until heated through. Serve with rice. If desired, sprinkle with additional chopped peanuts.