A few places in the parks MAY occasionally let you get a small item to go (for instance, Le Cellier sometimes lets people get the cheese soup to go). Some of the resort restaurants will sometimes let people pick up a meal. It depends very much how busy they are.
If you have a fussy child and have decided you need to leave mid-meal, any restaurant will pack up what's left of your meal so you can take it with you.
If you're looking to walk up to LeCellier or Mama Melrose's and order entrees to go......forget it. The kitchens just aren't staffed for that kind of a load. For instance, Le Cellier is very popular, and probably seats a couple hundred people (I'm guessing). There are many thousands of people in Epcot at any given time. If they allowed takeout, can you imagine how many people would walk up and want to order? Hundreds, potentially. They just can't do it.