The Stag scenes, my take.
To recap : Philip tells the Queen that he and the boys are on the trail of this magnificent 14-pointer stag. Later she comes across the animal unexpectedly in the countryside, and tells it to “shoo” before the hunters get there. Eventually, she discovers that it’s been shot by another party of hunters; and , in the end, the Queen visits the lodge where the shot stag is being stored, and kind-of pays her respects to the animal.
There are 2 reasons, I think, why these scenes were considered dramatically necessary.
First, and most important - these scenes give the Queen-character a chance to act in a manner the audience can sympathise with. You must remember that for the entire length of the film, she is portrayed as being “in the wrong” – in fact, she’s the films “baddie”. She’s shown as being completely out of touch with the mood of the country at the time of Diana’s death, and she suffers a catastrophic loss of popularity. All that was true enough, but the film required her character to show some redeeming features, just so that she didn’t come across as a complete pantomime villain. Weepy concern for the stag, and sadness at its death fits the bill nicely (never mind the fact that, in real life, she would probably have been the first to put a bullet into the poor beasts head.)
Secondly, the stag does stand as a symbol. The whole film is about a massive change that took place in the English people during that crazy week in 1997 when Diana died. The old stiff-upper-lip English reserve went right out of the window as the English people discovered in themselves the capacity to exhibit a very public, overtly demonstrative grief over the death of a much-loved public figure. Things would never be the same again. Those lingering scenes where HM the Queen stares sadly at the poor dead stag symbolise her grief at the passing away of the old order of things (or something like that).
Anyway, a fabulous film, deserving all its awards.