Have you seen this?
Is it possible that the Duchess of Cornwall might have said something to the Duchess of Cambridge that upset her? Yes, it is. The Royal family is a family and the same tensions and conflicts that can pop up in any family can happen in the Royal family. But relationships between the two of them are generally good, and they do like each other, so I would find it difficult to believe anything truly significant has happened here.
The Queen does not have the power to decide who succeeds her. That decisions is in the hands of Parliament. At the moment, if the Queen should die or abdicate, Charles, the Prince of Wales will become King and Camilla, Duchess of Cambridge, will become Queen Consort as a matter of law (although she may continue to use the style Duchess of Cambridge, just as she currently does even though she is legally the Princess of Wales). Even if Charles immediately abdicated in favour of his son which some people think might happen (I don't at this stage - if Charles doesn't come to the throne until he's 80, maybe), he would still be King until the instrument of abdication took effect and Camilla would still legally be Queen.
Frankly, I do not believe Camilla has any great desire to be Queen. She will do her duty when her husband becomes King, but it's not something that is important to her.
Further comments - in terms of Garvin's that neither Camilla nor Kate will ever be Queen because they are not in the bloodline, there are four different types of Queens. The Queen Regnant (which is what Elizabeth II is, what Victoria was, and what Elizabeth I was, among others) rules in their own right and they must be the Heir by blood to take on that role. But the wife of a King is also a Queen - a Queen Consort. Queen Elizabeth, the wife of King George VI (later the Queen Mother) and Queen Mary, the wife of King George V, are the two most recent examples of these. The third type of Queen is a Dowager Queen. This is a Queen Consort whose King predeceases her. So both Queen Mary (wife of George V) and Queen Elizabeth (wife of George VI) became Dowager Queens on the death of their husbands. The fourth type of Queen is Queen Mother, which refers to a Queen who is the mother of the current Monarch. George VI's wife, Queen Elizabeth used this title from the death of George VI in 1952 until her own death in 2002. (Queen Mary was technically the Queen Mother from 1936 till 1952 when her son died, but she chose not to use that style, instead continuing to be Queen Mary - Queen Elizabeth, the Queen Mother, naturally needed a way to distinguish herself from her daughter of the same name and so did use the title).
As for the body found at Sandringham, yes it was found on the Royal Estate. But the royal estate is 20,000 acres in size, part of which is land open to the public with hundreds of people travelling through it most days and with people actually living on it in normal English villages. There's no reason to think there's any link with the Royal Family. It may just be it was seen by somebody as a good place to try and dump a body.