Dear M.,
As a mom, I am normally not that discipline-minded. I always try to look for the underlying cause behind a behavior before assuming my child is manipulating me. BUT, in this case I'm going to go with the discipline crowd. Don't fall for the sad-faced thing. If your kids can sad-face you into serving them nothing but junk food, they'll wind up having unhealthy eating habits for the rest of their lives. That doesn't mean every meal has to be a showdown, but I would respectfully suggest that you're conceding defeat too soon.
So, definitely check out those hide-the-vegetables books. There's one other out there, that's supposed to be a little better than the Jessica Seinfeld book; sorry I can't remember the name. Also, get them to help you cook! Kids generally have a much healthier attitude toward food if they're involved in preparing it, not just consuming it. If you can (I know this starts ambitious) start a little vegetable garden and have them really work with you. They'll probably like watering it with the hose, if nothing else. Foodie-types swear that kids will eat anything they grow, even kale(!)
But, at the bare, bare minimum, try to design one healthy meal that they will eat -- pasta with organic frozen meatballs and green beans doesn't sound that bad, especially if you can bury some whole-grain pasta under a whole lot of pasta sauce. (For my son, I actually put pasta sauce and tofu together in the blender, since we don't eat much meat.) If that's the only healthy-ish food they'll eat, just cook that every night. When they get tired of that, have them sit down with you and choose another reasonably healthy dish to cook together (you can probably squeeze some vegetables into a lasagna, for example.) Whatever you do, don't let really unhealthy foods like chicken nuggets (sorry!) be an option.
I know this won't be easy, especially with twins, since they tend to reinforce each other's behavior. But don't give up!
All the best,
Mira
P.S. Oh, and if they absolutely won't eat any greens, would they drink "green smoothies"? Orange juice, banana, mango, and spinach in the blender. Tastes like dessert, looks like a St. Patrick's Day parade, and is amazingly good for you (just don't tell them that!) :)