Hi Shelby:
As an adult, I've ordered off the kid's menu at Disney World on a number of occasions without issue. While technically the restaurant will have the final say, I also know of many other adults who have ordered off the kid's menu without any incident (and without a doctor's note). Indeed, fellow Disney mom Anna, who had gastric bypass surgery, also has
never had an issue with ordering off the children's menu. However, I encourage you to bring your doctor's note, just in case.
Other than for children under three, I've never seen sharing allowed at a buffet or family style restaurant, but it will be up to the individual restaurant. So if you choose to take the chance that you may be charged full price at a buffet or family-style restaurant, I would bring the doctor's note and ask if you can be accommodated (both when you make the reservation and when you arrive at the restaurant). In the worst case scenario, my children were able to order peanut butter and jelly sandwiches at family style restaurants when they did not care for the food on the regular menu, so there are off-menu options available if you ask.
Good luck and enjoy your vacation.