This story is set years after The Vampire Diaries' Graduation episode and the House of Night series. I've altered the storyline of the TVD (season 4) to my liking. Most of the House of Night will stay exactly the same.
After Elena turned her humanity back on, she was still angry at Katherine, but still didn't think it was worth it to kill her.
The cure never left Katherine's possession, when she gave the cure to Elijah to prove her love, he gave it back to her before he left to New Orleans with Klaus.
Instead of trying to shove the cure down Klaus' throat to kill him, Katherine gave the cure to Klaus in exchange for her freedom.
Katherine is the one to save Elena, Stefan and Caroline from the witches that Caroline killed.
Bonnie makes Katherine immortal in exchange for helping her friends, and a promise that Katherine will not hurt any of her friends (which Katherine would happily do if it meant she can live forever, which means that the Kat/Elena fight never happened).
Klaus came back to Mystic Falls to put Silas in the safe and throw him in the quarry himself.
Bonnie did the spell to bring Jeremy back from the dead, but didn't succeed and died herself. Her and Jeremy ended up at Nyx's Otherworld eventually and stayed there happily, watching over their friends and family.