If a murder mystery involves a rich family, there is an excellent chance that only one of them will get along with other human beings and at least three fourths of them will have manners so bad you’re surprised that they are not frequently punched in the face. I suspect that there are three reasons for this.
The first, and most mundane, reason is that it’s a trope. Merely because it has often been done before, it will be done again. Many writers, especially in television, are lazy and unimaginative. There’s not much to say about this reason, but I do need to acknowledge it.
The second reason has to do with the needs of a mystery story—there must be suspects. When a rich family gets along like cats and dogs it produces a lot of suspects. It’s true that this shows everyone as having a motive—whoever dies, everyone else hated him—but it also shows that no one in the family has the sort of self-control which makes you think that they would refrain from murder because of their principles, if they had any.
The third reason is the most sinister. Most writers are neither rich nor know for their extraordinary resistance to envy. Even if not personally envious, they are not proof against trying to flatter the envy of their readers. It would be, more specifically, sour grapes, but sour grapes are generally an expression of envy. I suspect that this is no small part of why this is a trope.
Now, speaking generally, there is nothing wrong with including spoiled children in a story, nor in including family members who do not get along. I do gravely doubt that the children of the rich are often casually rude; when you don’t have many problems, upsetting other people looms much larger in one’s field of view. In my experience, casual rudeness tends to correlate to being raised by absent or single parents, in poverty, where other people’s feelings seem quite small in comparison to more pressing issues. One really needs to have a lot going wrong in order to be unconcerned about unnecessarily offending others. (Which is not to say that rich people can’t generally pay for their problems to go away, only that upsetting a person is an immediate problem that one feels immediately because man is a social creature. Treating someone badly when out of sight and using money to paper over the problem—that is very easy to believe of someone raised rich. Treating them in a way that makes them upset with one in the moment? That is far less believable.)
However that goes, this does not tend to make for a really good mystery, however, because the characters are not interesting. Characters are interesting because of their virtues; vices can only help when they serve to highlight virtues. Merely being a failure of a human being is boring, and when there are no characters who are not failures—there’s nothing interesting to read about.