Anyone can order off the kids' menu. The restaurant might charge more and up the portion size for an adult (that's the rumor going around about some of the WDW restaurants- who knows if it's true?), but since you are on the Dining plan, and you are paying adult prices anyway for your 10 year old, there should be no problems.
Think about it from Disney's point of view: they got you to pay for the adult price. If your 10 year old orders kid food, great! More profit for them. I'm sure mac & cheese, hot dogs, and chicken fingers cost way less to prepare and serve than steak and shrimp.