Most restaurants will allow anyone to order from the kids' menu, but ask first because there have been reports of a few that did not.
If your child orders from the kids' menu you can ask about increasing the portion size for the entree if you are using an adult dining credit. If the restaurant will not upsize the entree consider paying OOP for the meal and save the adult credit for additional meals or 2 credit meals.
When using an adult credit, but ordering from the child's menu some will let you order the dessert from the adult menu while others will not. How flexible a restaurant can be is often based on whether it is Disney owned or a third party restaurant that gets reimbursed by Disney based on the rules of the dining plan.