H.C.
You're the mother; you're in charge. Want them to have dinner at the table without t.v.? Then that's how they have dinner, or they don't eat. Period. (Don't feed them later, either, when they're hungry.) They will NOT starve.
Yes, you should stress about it, but not for nutritional reasons. Do not let them dictate how the family functions. It may mean reducing or eliminating their television time as well.