The GAC has no part in this. GACs are used for accomodations in parks. They are not used in restaurants.
As the others have said, anybody can order off the kids menu without having to give a reason. I will say though that she'll likely get very tired of this as the offerings are not that great and with her goals with the band surgery, not really the best options. She can order appetizers or sides or share meals with you. This is totally aside from the DDP though.
At fixed price restaurants (buffets, character meals, shows), I would go in expecting to have to pay full adult price. The only reports I've read of people being charged less are people who basically don't eat anything at all and even then it's hit or miss since it's up to the discression of the manager.
The DDP is not for everybody. My family likes it a lot but we can't share meals easily (different people have different food allergies and special dietary needs) and some of our meals would have an up charge because of the nature of the meals (certain allergy foods cost more) but on the DDP they're just a single credit. It works well for us. For somebody who prefers appetizers or kids meals or can share meals regularly and won't want dessert (all of which it sounds like would be your wife's situation) I would advise against the DDP.
If you do still want the DDP, you can make it really work for you if you think about it. She can order an appetizer or side which you pay for OOP. Use 1 credit to pay for your meal and she can sample your dessert (I'm assuming she won't want a full one of her own with her diet goals and inability to eat much). This basically doubles your number of meals. For lunches, she can easily eat with a snack credit (thinks like egg rolls or fruit can be purchased with snack credits; take a look at the confirmed snack list on the DDP board) while you order a full lunch for yourself.