Mix cabbage, apple, carrot and onion in a large mixing bowl. The apple is optional, but I would advise trying it, it makes the coleslaw so much better. Dice the apple into a bowl of salted, warm water first and let it sit for a minute or two, then drain. This keeps it from turning brown and the slaw can be kept for two to three days in the refrigerator if you have leftovers.
For the dressing, combine the sugar, water and vinegar and microwave for about 3 minutes or cook over medium heat in a saucepan until it comes to a boil and boil for a minute or two. Set aside and cool completely. You can place it in the refrigerator to cool it faster.
Once cool, stir in the mayonnaise, the honey mustard and the yellow mustard. Pour the dressing mixture over the shredded cabbage and other ingredients and mix well. This is best if you refrigerate for at least 2 hours for the flavors to blend. Stir again right before serving.