Yes, Lady Macbeth kills herself (according to Malcolm at the end, anyway), but not until right near the end of the play, when the approaching army has already cut the branches to disguise themselves. And that idea comes from Malcolm, the rival for the throne (Duncan's son), whose army it is - Macduff is an ally of Malcolm.
To say that the story doesn't completely gibe with the historical events of Macbeth is an understatement - Macbeth reigned for 17 years, and the kingdom was peaceful enough that he could go on pilgrimage to Rome. He was killed in battle against Malcolm's forces, but he was succeeded by his stepson Lulach (ie the son of "Lady Macbeth" - her real name being Gruoch). The absence of Lulach from the play really makes it a story that has just taken the names of historical characters.
As for the real world, I see nothing that indicates Vance will pay any attention to Pope Leo. Everything he's done indicates he is immoral, and fits well into the court of Trump, but there's zero chance he could overthrow Trump - we've seen that no Republican stands up to him, let alone a majority of the cabinet and a third of the Republicans in both houses of Congress, as invoking the 25th amendment would need. I have no idea what "Trump's son-in-law, Eric Prince" is supposed to mean.
I think you're far too generous to Vance. He's a conniving bastard. If he did become president (by Trump dying), he'd collect his own sycophants. He won't "rebuild" anything. He won't have the hold on Republicans that Trump has, though.