A tantrum like that would have cost my children a black and blue bottom, regardless of whether it was in public or not!
Problem is now you would have likely been arrested for child abuse and your children taken by authorities after the flight turned around because of an abusive parent. It is hard to be a parent these days. My daughters are hesitant to correct their children at all in public. There is always one person claiming child abuse for even a raised voice. I am glad I am not raising children now because the spotlight is really on parents.