If it is just the arguments I can give some tips. First off it sounds like your mother is set in her thoughts and becomes aggravated when someone tells her otherwise. It sounds like your father avoids upsetting her, or avoids confrontation, and takes the short and easy way out.
Depending on who you try to debate with it becomes an argument. I like to debate and see others points of view, however most don't see it that way. When one states their own points the other usually mistakes it as being told they are wrong. I think that is how your mother takes it and becomes angry for being told she is wrong.
So I don't think a mediator would be feasible in this situation. The easiest way would just to end the arguments or discussions. I usually notice when someone starts becoming aggravated I change topics or end the discussion. Though it took me a while to notice since I pissed off a lot of people before.
I personally think
>>2 is kind of right. I think it has more to do with being open minded to others views, or opinions. I am very open minded and it is very hard for one to insult me. I guess I am an adult, 23, and I still take advice from anyone, younger or older. Though if someone is closed minded they might be even more upset when someone younger offers their own opinion. Being younger, to them, would kind of mean they experienced less of life in a way. But I don't think that is why your mother gets so upset.