Instead of discussing what in all probability would happen, I say, we should just try to come up with something really funny.
Like, have Diana get involved more and more into political causes, leading to her joining Labour under Tony Blair, and being elected to Parliament, finally making it into the cabinet. Brown still loses in 2010, but this time, it isn't a Miliband that takes over the Labour leadership, but ex-Princess Di, who leads Labour to a landslide victory in 2015.
And now, as Prime Minister, she begins engineering to get her revenge! Like, proper House of Cards style!