Story Changers/What If Darth Vader Raised Luke and Leia?

Transcript
A long time ago in a galaxy far far away, Padmé Amidala recently gave birth to two children: Luke and Leia. Unfortunely, she passed away shortly after as the father, Anakin Skywalker, was there before fighting Obi-Wan, leading to his fall and becoming the Sith Lord known as Darth Vader. Being motivated, he searched for his two children before finding his former master trying to ship his children off. He and Obi-Wan face off in a second duel as Vader succeeds taking his children with him. Soon, they begin training under him at the age of ten in the dark side of the force. Later, when they became preteens, they were taught about the power of the Dark Side of the Force as they learn how to use it while he enforced the Empire's rule, hunting down everyone who opposed the Empire's rule. Without the last hope to disband the Empire, Obi-Wan risks everything by secretly infiltrating as an Imperial officer to take down the empire. Unfortunately, Vader found about this and became extremely mad with it as he ordered his children to fight him and eventually kill him. However, as they first met, Obi-Wan warned Luke about not letting the Dark Side taking him over as he could be the one that could bring his father back to the light side. Before he finishes, Leia is behind him and stabs him. Obi-Wan slowly dies as they look at him without any guilt.
 * Obi-Wan: Young Skywalker, don't do this, there's another way.
 * Luke: Lies! My father warned about the menace you could represent to the Empire.
 * Obi-Wan: That's where you're wrong. Your father used to be one of us. He was the chosen one. But then, he grew power-hungry and he eventually got corrupted by the Emperor and forced to enforce his rule.
 * Luke: What if I like the power?
 * Obi-Wan: Do you want to hear what actually happened to your mother?
 * Leia: Your time is over, old man. I won't let my brother get manipulated by your lies.

Considering that Luke ended up in the Dark Side with his sister, how would the Empire collapse? Simple, [Han Solo].