Cersei grew tired of the marriage and wanted to pass on formal rule to her son (though not her husband's). Cersei also needed to get rid of the hopelessly honest Prime Minister who made the mistake of informing her he intended to tell the King of her adultery and incest.
Although in the long run things didn't work out for Cersei and her family, in the short run they do. No one is ever punished for the hunting accident; Cersei and company jack the throne and keep it for most of the story.
In real life, hunting accidents during the Middle Ages were one of the normal explanations used to cover up rather obvious assassinations. William Rufus, King of England from 1087-1100, was the third son of William the Conqueror. So he wasn't expected to inherit very much. But life has a funny way of unfolding. Richard, one of William's elder brothers, died in what was evidently a legitimate hunting accident.
Shortly after that William Rufus and his younger brother Henry decided it would be amusing to play a joke on their oldest brother Robert, who was William the Conqueror's presumptive heir. The two young men emptied a full chamberpot on Robert's head.
Unsurprisingly Robert didn't appreciate this "joke". Robert was incensed when his father, King William, refused to punish his younger brothers. Robert showed his displeasure by starting a rebellion. When that failed (would you be all that interested in following a leader who probably still smelled like s***?) , Robert started a ten year campaign against his father's interests, making common cause with the French, his father's enemies.
This decision led to further rebellions by Robert's partisans in England, including some of William Rufus' and Robert's relatives. Eventually William Rufus stamped out the revolts in England. William Rufus went to Normandy and defeated his brother Robert. He did not kill him. The two made up for a time.
However William Rufus wasn't keeping a close enough eye on domestic enemies. As King, William Rufus was a religious skeptic. Worse, from the church's point of view, King William Rufus confiscated many churches, their lands and revenues for himself.
When a bishop or archbishop died William often refused to appoint a new one at all, or at least until he could be assured of receiving sizable kickbacks. This infuriated the church. Lastly, William Rufus was gay and rather publicly so. There were clergy who preached against what they saw as the King's wickedness.
In 1100 William Rufus and his younger brother Henry took a hunting trip. The King became separated from the main party. He was alone with the nobleman Walter Tirel, a family friend and skilled bowman. To hear Tirel tell it, he was shooting at a stag when the King got in the way and was hit right through the lungs. Horrible accident, you know.
Well maybe. But Henry and friends didn't even bother to pick up William Rufus' corpse. The body was left to be found by a peasant. Henry made a beeline to the Treasury to seize it before having himself crowned King the very next day. And Tirel was never punished. So I guess the moral of that story is relative or not, be careful going on hunting trips with people who badly want something you have.
