How would Albus Dumbledore and Severus Snape have machinated Dumbledore’s demise, if Draco Malfoy had failed to amend the Vanishing Cabinet?
Probably without too much difficulty; they would have orchestrated some confrontation whereby the two appeared to duel, with Severus managing to get in a final killing curse.
...somebody... ...had spoken Snape’s name... “Severus...” (Dumbledore) The sound of frightened Harry... Snape gazed... ...at Dumbledore... “Severus... Please...” Snape raised his wand and pointed directly at Dumbledore. “*Avada Kedavra!”* ...Dumbledore... ...fell slowly backward, like a great rag doll, over the battlements and out of sight. Harry Potter and the Half-Blood Prince - J.K. Rowling
One can just imagine what might have occurred if Dumbledore had raised his own wand.
Circumstances and location would have been different, if Draco had never succeeded with the Vanishing Cabinet.
Can you envision a scene whereby Harry and Albus have returned to Hogsmeade after their trip to the Cave by the Sea, with Death Eaters awaiting them at the Hog’s Head Inn?
Voldemort having run out of patience and deemed Draco’s endeavor a complete failure, the young Malfoy having been banished to the Slytherin Common Room until the events play out, the Dark Lord giving Snape the go ahead to begin bringing Death Eaters into Hogwarts via a secret tunnel Snape had mentioned as an entrance.
That confrontation between Voldemort and Draco had not gone well; Voldemort had expected Draco to fail, but had to show fury at the planned disappointment in front of the other Death Eaters; Snape had only brought it up as a last, deft move to distract Voldemort from crucifying Draco in front of the other Death Eaters and Narcissa Malfoy.
After suggesting Malfoy be returned to Hogwarts so as not to raise Dumbledore’s suspicions, Snape mentions that he is aware that Dumbledore had left Hogwarts that particular evening, though Snape knew not where, only that the headmaster had apparated from the Hog’s Head.
Dumbledore’s brother, Aberforth would have taken down a number of Death Eaters as they entered his tavern unwelcomed and unannounced, but eventually, between Amycus Carrow and Fenrir Greyback, the younger Dumbledore would have been subdued.
And then... Dumbledore doesn’t appear. After a time, Bellatrix Lestrange and Amycus question Snape, who tells them to stay put. Severus knows Dumbledore has a friendship with Madam Rosmerta and suspects
Harry and Albus may be there. A brief disapparation and Severus is inside the Three Broomsticks, in the shadows, just as Harry and Albus arrive.
Immediately seeing that Dumbledore is in a weakened state and having to keep up pretenses, Severus casts a Full Body Bind spell upon Harry and separates him from Dumbledore.
Severus allows Dumbledore to apply Legilimency again, as they have done for seventeen years; that is one of the ways Dumbledore has always confirmed Snape’s allegiance to him. Then, for Harry’s benefit, they speak.
“So, it has been you working against me all this time, Severus,” says Dumbledore.
“For much longer than even you might realize, Dumbledore,” is the reply.
“I’m sorry, but I will not be able to appease Voldemort by allowing you to take Harry tonight, Severus.”
And with that, Albus casts his first, deft spell, though in his weakened state it is both delayed and less powerful than it might have been otherwise; either way, Snape easily avoids the spell by disapparating and apparating, around Dumbledore, again and again, until the headmaster, still dealing with the magically poisonous water from the cave, can not raise his wand any longer.
Severus had opening after opening to cast the Killing Curse, but he cannot bring himself to point his wand at the only comrade he has left in the world; it’s as if his wand is made of lead.
But, finally, Dumbledore, having fallen to his knees, bearded chin dropped to his chest, still repeats that phrase... “Severus... Please...”
And finally, Severus screams, “Avada Kedavra!” in a voice filled with as much pain, as anger for having to be responsible for the death of someone else close to him.
Harry cries, “Nooooo!!!...” as Rubeus Hagrid bursts through the door, Minerva McGonagall and Filius Flitwick close behind. Spells and curses fly at Snape, who immediately disapparates and the deed is done.
Death Eaters flee as well, as the remaining staff at Hogwarts has come down upon them in the Hog’s Head.
But Dumbledore is now dead, Snape’s Unbreakable Vow to protect Draco still intact and Harry, as well as all of the staff and student body at Hogwarts now believe Severus to be the traitor and Voldemort’s most powerful Death Eater.