Preheat oven to 350 °F. Place chicken in the bottom of a 13x9x2-inch baking dish or 3-quart rectangular casserole. In a large bowl, combine broccoli, rice, and peas. Spread mixture over the chicken. In a medium bowl, combine cream of chicken soup, nacho cheese soup, diced tomatoes, milk, and crushed red pepper. Stir in 1/4 cup of the cheddar cheese and 1/4 cup of the mozzarella cheese. Pour soup mixture over broccoli mixture in baking dish. Sprinkle crushed crackers evenly over all. Top with remaining cheddar and mozzarella cheeses.