Combine the green and red cabbages, carrots, and green onions in a large mixing bowl. 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 vinegar, sugar, 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 transfer to the refrigerator for 20 to 30 minutes.

In a small bowl, combine the mayonnaise, sour cream, horseradish, and mustard and stir to combine. Add the mayonnaise mixture to the coleslaw and toss to thoroughly combine. Cover and refrigerate for at least 1 hour and up to overnight before serving.