My wife, on a reduced carb diet, had NO problem whatsoever eating at Disney. But, having said that, we were having all table service meals.
She alerted the waiter at each restaurant, who typically had ready made suggestions for her. I have to say, however, that most of these waiters weren't that familiar with diabetes and what "reduced carb" means, unlike those with peanut allergies (which apparently, they understand VERY well). They'd suggest entrees with rice and potatoes, without suggesting to replace the starches with vegetables. They'd suggest the sorbet, which is actually higher in sugar than regular ice cream.
You need to reduce or eliminate the starch portion of each meal. You'll also avoid any sugar laced sauces. If it looks like cake or bread, you'll push it to the other side of the table. You'll ask for starches to be replaced with green vegetables, and at every table service, they'll be happy to do so for you. You'll ask for the salad dressings and sauces "on the side" to allow you to limit how much goes on your food.
At 'Ohana, you will not be having the dessert, but you can have all the shrimp and beef you can eat. You should limit the pot stickers to one or two, and not have the wings (unless you can remove all the bbq sauce). You'll pass on the noodles, and have the vegetables. You'll limit your chicken and pork to one or two pieces, unless you can remove all the bbq sauce.
At Crystal Palace breakfast, you'll have to skip the breakfast lasagna and all the pastry, but can have the eggs and meat. You'll skip the breakfast potatoes, but can have a helping of strawberries and blueberries, but not the cantaloupe or honeydew melon.
You'll want to think about getting an app for your smartphone, like myfitnesspal, which will give you ballpark numbers of carbs and sugars for typical servings of normal foods, and learn how to identify carbs and sugars in the descriptions of foods in order to avoid them.