In a large mixing bowl, combine the green and red cabbages, carrots, and green onions. In a small bowl, toss the cubed apples with the lemon juice and add to the cabbage mixture.
In a small mixing bowl, combine the sugar, vinegar, salt, and pepper and whisk until the sugar is dissolved. Pour the seasoned vinegar mixture over the cabbage mixture and toss to thoroughly combine. Cover with plastic wrap and refrigerate for 20 to 30 minutes.
In a small bowl, combine the mayonnaise, sour cream, horseradish, and mustard and stir to combine. Add to the coleslaw and toss to combine thoroughly. Cover and refrigerate for at least 1 hour or overnight before serving.