If the intrigue made any sense, or been more dramatically structured, it would be worthy of Hamlet. That's the point. It doesn't make sense and you frankly don't give a toss. I am not an historical purist. That is not the problem here.
Movies are neither inclined to nor capable of telling 'the truth' about historical events.
At best, filmmakers deal in emotional truths and play with facts to telescope complex situations into a dramatic vehicle that audiences can drive without a licence. Kapur did do that when he burst on to the international scene with his Indian biopic, Bandit Queen. Elizabeth lacks the panache of that film. That said, Kapur does a splendid job with the look and feel and even the perceived smell of the new film. He is a master of mood and atmosphere.