Combine marmalade, soy sauce, vinegar, hot pepper sauce and cornstarch; stir to dissolve cornstarch. Set aside.
Place large skillet or wok over high heat for 1 minute, then add oil. Heat oil for 30 seconds then add ginger, garlic and shrimp. Stir fry for 2-3 minutes. Remove from wok and set aside. Add bell peppers and broccoli, cook for 1 minute. Add water; cover and reduce heat for medium. Cook 4-5 minutes.
Uncover and heat to high, add shrimp, marmalade mixture and water chestnuts. Cook for 2 minutes.
Season to taste. Add green onions. Serve over hot cooked rice.