To get through this particular one day, I'd eat something small from my abstinent meal plan (say, the fruit part) around noonish like usual. That should hold you until you get your meal. This is not ideal--well, not on my abstinence, anyway--but sometimes concessions must be made.
In the future, you don't have to explain anything about it. You don't have to say you're in OA, you don't need to elaborate about your food plan, nothing. Everyone's in charge of taking care of their own body, and if your body is hungry, it needs to be fed. If your aunt wants to make plans in the future, you could say something like, "you know, a bit earlier in the day works better for me. Can we make it noon?" and just leave it at that.
IT IS OKAY TO SPEAK UP FOR YOURSELF!