S.M.
Take them out to the car and put their seatbelts on. One of the adults can sit with them, while the family enjoys the meal. My husband and I do this with our toddlers, which is why I believe our know 6 and 2 year old don't misbehave at the table. At home, send them to their rooms, or better yet to seperate rooms with no toys. They get one more chance ot apologize and be reseated, otherwie no more food, no dessert. And then you need ot actually follow-through.
Frankly, I don't really understand this seems like such a challenge for you? You may feel bad for making them leave, but it will only take a couple times. No, they don't need to be physically assaulted for acting like children (as mother suggests) not are they necessarily spoiled (as Daddy suggests), but they cannot be allowed to continue to act out that way without consequence and without realizing it effects everyone. It's simple, you can't behave at the table then you need to leave. Simple direct and relevent consequences.
And an additional note, sit them seperate from one another if they cannot cooperate and invest in a couple little bags with some quiet dinner games, books, activites. Additionally, do they know wha tgood manners are? Do you tell them to sit on bottoms, put napkin on th lap, speak in an inside voice, not wiggle and squirm, no grabbing food, say please and thank you?? Sit downa nd ask them to help you write a list of expectations fo rmeals with you.