Wow, I have AS and I acted (well I suppose I still do to a lesser extent) just like your kids when I was younger, including those specific arguments (finish the food, come downstairs), and until I just heard you comment on how ridiculous those demands were, I thought for sure it was just my mom who was the one acting irrationally. Whoops, I think I owe my mom a hug and an apology.
One thing I still don't understand though, is why it's so important to finish ALL the food on your plate. Whether you eat it or not, it still just goes to waste in the end.