I don't know if this would work with everyone's children, but it's what we did with DD.
I got so sick and tired of every meal being interrupted with corrections and rudeness, that I finally started feeding her alone and then having dinner with DH later (while she was still awake). I made it clear she would be welcome back at the family table when she was able to conduct herself in a manner befitting and that also, until she was able to behave herself, that meant anytime DH and I wanted to dine out, she'd have to remain at home with a sitter.
Luckily for us, she was miserable having to eat alone and it only took a couple of days of that before she decided to shape up. All I have to do now is threaten to serve her alone and that usually stops it. If it doesn't, I excuse her from the table to her room, and she is allowed back after we've finished our meal and eats alone. I think I've done that maybe 2 times.