I am coming from a position where this hasn't happened to me personally, with my children. However, we came close with ex-boyfriend when he was staying with us. He had the sense to not say things in front of me.
If this were happening in my space, I would step in at least to referee. That is when I would get each of them a sheet of paper and ask them to write down the arguments that THEY wanted and to also write down the arguments they thought the other person would use to get what they wanted. The ground rules are, no put-downs permitted if not relevant to the argument. In other words, differences in taste must be accepted as just that - differences - and not a reason for personal criticism. However, it IS permissible to put in writing these arguments if you feel they are relevant or if you feel they are arguments the other person will use.
Then the papers are shown. Depending on the personalities, I would read them out rather than the author. No recriminations, no anger. Often the author of the arguments feels ashamed at this point. Also, if the arguments have been sufficiently long-standing for the other party to be arguing just as inappropriately, this is a useful process to get BOTH of them back on track to healthy arguments.
husband & I sometimes argue in front of his mother, but we argue in a healthy way. At first she used to be upset until she realised we were just being ourselves and that it was healthy.
What is important in refereeing - pulling the rug on inappropriate arguing, but allowing arguing that is healthy and moving to a good conclusion. The personal attacks are not appropriate. Attacking the choice probably is.
For example, we have some money come in from our tax refund. What should we do with it? I might want it spent on shares because right now is a great time to invest in the share market. husband might say, "No way! People have taken a bath on the market! It's like gambling! No, we should invest it in ourselves, and pay off the mortgage."
If husband says to me, "Are you crazy, woman? What kind of fool do you take me for?" that is NOT driving the argument forward. I have not, in my suggestion, given any indication that I think he is a fool. But now he has mentioned it... the gloves come off.
And this is what can happen - a bad argument can quickly escalate until both parties are at fault. The original argument is lost in a lather of personal attacks and everyone retires, hurt. Nothing has been achieved and much has been lost.
Some people have never learned how to argue properly. Some people (especially some males) have grown up with the belief that the man has to make the decisions, that he has to constantly battle against the woman's tendency to spend money like water. A man must always provide for his family and take pride in his wife, LETTING her spend money like water because her appearance is a reflection on him and his success.
Not good. Very bad, all round. Because he will always take an adversarial position and always belittle, trying to force her back into the role he feels she should never have left.
Some women have grown up with men like this and have learned how to manipulate and wheedle. Again, not good.
For a couple who need to learn how to argue - I recommend the rules of debating as a good start. If only one partner is prepared to make changes, you can still bring change, but you need to go to conflict resolution techniques. make "I" statements, not "you" statements. For example, "I felt very hurt when you told me I was a fat pig with no right to a personal opinion. I also didn't feel that what you said as relevant to what we were trying to discuss - where to send our child to school."
You DO NOT say, "I'm a fat pig, am I? So what does that make you, you lazy, good-for-nothing lump of lard!"
Schooling options are now completely forgotten.
You do not have to be wealthy to put on a 'good spread'. I tell people - I specialise in gourmet poverty food. I have ordered, in restaurants (for a huge price that thankfully someone else was paying) a meal which I can whip up in my kitchen for a fraction of a dollar per serve - gnocchi alla Napolitana. If you plan ahead, you can provide tasty nutrition as well as ample serves. But what is even more important - your home should be a sanctuary from unpleasantness and personal attacks.
Chances are he is arguing the only way he knows how, the way he has been taught. I would say quietly to him, "I don't know where you learnt to debate, but in MY presence, you will be polite to your debating opponent and you will stick to the subject. That rule goes for everybody - we all must feel welcomed here, must feel safe and accepted here. Everybody."
He may not even realise how wrong it is.
Whenever I am in doubt, I think back to how my mother would have handled it. She wasn't perfect, but she tried to be. And in trying, she set us some very high standards of behaviour.
Good luck with this one. By staying silent I think you are showing him that what he is doing is OK. And you're showing your daughter that she must also stay silent. Not good.
Maybe read up on conflict resolution first, talk about these techniques with your daughter and practice them between you, so you are good at it before you try to teach him.
Marg