"One very bad habit in many families is the discussion of all of their most intimate affairs at the table-entirely forgetting whoever may be waiting on it; and nine times out of ten those serving in the dining-room see no harm (if they feel like it) in repeating what is said, Why should they? It scarcely occurs to them that they were "invisible" and that what was openly talked about at the table was supposed to be a secret!
Apart from the stupidity and imprudence of talking before witnesses, it is bad form to discuss one's private affairs before any one. And it should be unnecessary to add that a man and his wife who quarrel before their children or servants, deprive the former of of good breeding through inheritance, and publish to the latter that they do not belong to the "better class" through any qualification except the possession of a bank account.
Furthermore, parents must never disagree before the children. It simply can't be! Nor can there be an appeal to one parent against the other by a child.
"Father told me to jump down the well !"
"Then you must do it, dear," is the mother's only possible comment. When the child has "jumped down the well," she may pull him out promptly, and she may in private tell her husband what she thinks about his issuing such orders and stand her own ground against them; but so long as the parents are living under the same roof, that roof must shelter unity of opinion, so far as any witnesses are concerned." --Etiquette by Emily Post
I have had waiters and waitresses stop and listen to my private discussions. Not that they were particularly private but it is still quite rude. Waiters and waitresses are not invisible but they should not interfere or listen to a private discussion that do not concern them. I have also experienced waiters and waitress share very personal information with me. For some unknown reason people love to share personal information with me. Most of the time it is amusing.
Now on the matter if parents arguing with each other in front of their children I agree with Ms. Post. But if my child came to me and told me that their father had told them to jump in a well I would assure them that he was only kidding and privately ask my "husband" why he issued such an order. It is very inappropriate for a husband wife to quarrel in front of anyone. It happens yes but out and out fights are in very bad taste. Quarrels and fights are private matters and should not be broadcast.
Another matter that Ms. Post did not address, children quarreling with their parents in public. Or at all for that matter. Discussions are appropriate in private as long as the do not turn into arguments. While a child is lives under their parents household they are subject to their parents no matter how old the child is. Respecting ones elders is very important.