We went last year and I simply told the server that I was vegetarian and she said she'd bring me a separate vegetarian meal. I also asked for no dressing on my salad and she brought me my own bowl of that as well. Everyone else in the family eats meat (and dressing) so they were served all of the normal stuff.
I was brought a huge platter all for me with a veggie loaf (looked like a meatloaf comprised of veggies and stuffing with a tomato glaze on top), mashed potatoes, veggies, fries, and there may have been rice as well. I also had my own bowl of salad as requested, the shared platter of dinner rolls, a shared bowl of Mac and cheese topped with goldfish crackers, and the standard berry something dessert.
I thought the veggie loaf was absolutely delicious. Everything else on the platter was fairly standard, but still good comfort food, and it was really appreciated that it was brought on it's own platter, separate from the meats. I was told just like the rest of the table that if I wanted more of anything to just ask, but the platter was so huge it wasn't necessary.
For the regular platter, the meats, mashed potatoes, veggies, and stuffing all came out on the same platter and everything was touching. The fries, Mac and cheese, rolls, salad, and of course dessert all came in their own separate bowls/plates. They did ask if the kids were okay with the foods touching before bringing the platter out, which was a nice touch, though my kids don't mind so we told them it was fine. If they don't ask, I'm sure you can request to have things brought out either on separate plates or not touching. The server also discreetly asked if we would like some plain chicken legs made for the kids, but we declined.
Overall, the restaurant seemed so accommodating, the food was great, and we had- by far- the BEST character interactions ever.