EDIT 8/2/16: New more accurate summary (contains some vague spoilers):
The life and journey of Harry Potter from an emotionally stunted and angsty war survivor with waaay more power than he needs into a (semi-) mature adult. This will start out with a bunch of flashback like chapter intros to show how his life diverged from the cannon story-line (mostly due to a Dumbledore who was actively preparing Harry for war, and a much more introverted and independent Harry). These flashbacks will be occurring alongside Harry's life in Forks Washington, where he will become tangentially involved in the plot and misadventures of the Twilight series. However, this will end up being a minor part of the story, as Harry quickly moves on to interacting with the Stargate cast and universe (after a seven year time skip). The only Twilight character that will continue to show up in any meaningful or consistent manner will be Seth Clearwater, with whom Harry will eventually have some degree of romantic relationship - haven't gotten there yet.
-October 31st, 1997-
Harry Potter and Albus Dumbledore stood side by side atop the astronomy tower staring down and across the savaged grounds of Hogwarts, strewn with the bodies that had not yet been cleared.
"It's done then. He's dead."
"He is indeed dead," Dumbledore replied tiredly.
"Then the bindings are broken."
"That they are," Dumbledore sighed.
"Then I'm leaving."
"I had expected you would." Dumbledore replied, sounding defeated.
Without any more words passing between them, and indeed with only the slightest whispers of sound Harry Potter vanished from the tower, leaving Dumbledore alone.
"Someday Harry I hope you can understand why I did what I did, and I hope that on that day you can find it within yourself to forgive me." Dumbledore spoke to the empty air, already knowing that Harry was long gone. "It would be more than this old man deserves."
- Seven Years Later -
Harry stood alone in the bustling crowd of people on a street of New York City, looking down at the news paper in his hands. It proclaimed rather loudly and excitedly in bold font the heart attack of 'The Great Albus Dumbledore', and the fact that even now it was only magic that was sustaining him. Harry sighed as he looked up into the sky between the skyscrapers, allowing the wind to whip by him and burn his smarting eyes as he stared directly into it. He glanced at the paper once more before striding quickly over to the nearest trashcan and leaving it there; his decision made. He shuffled through the crowd until he reached the opening of a relatively dark and narrow alley, he took only a dozen steps into the darkness before spinning about and making only the briefest of inspections of the passing crowd to be sure he was unobserved as he vanished.
He reappeared in a corner of the Hogwart's Hospital Wing, invisible and with a tight control over his aura so that even Dumbledore would never be able to sense him from more than a couple feet away. The room was empty but for a curtained off section near the back. Harry strode towards it on silent feet only the slightest of hesitation before the curtains betrayed his apprehension. Slipping between them harry stood silently, observing what had become of his mentor these past years. It seemed to him that time had truly and finally caught up to Dumbledore, as his locks of silvery hair had become a dull grey and his creased face had taken on a chalky pallor that served to emphasize his many wrinkles. His breathing was shallow and Harry could tell that, though his eyes were closed, he was awake and likely occluding to suppress the pain. Navigating around the bed harry allowed himself a sigh as he sat in the chair at his bedside and released his invisibility even as he reached out with a tendril of his aura and caressed Dumbledore's own.
Dumbledore sighed, and even without opening his eyes spoke in a wearied and breathy whisper, "I had hoped I would see you again, before the end, my boy. I am glad you found it within yourself to come see me off."
The silence stretched for a moment before Harry spoke, "I may hate you for what you did, but I love you for it too. You took my childhood and much of my choice in life, but in return you gave me a mentor and a friend, and, in the end, you gave me my freedom and the world." Harry could see Dumbledore's emotions swirling beneath the surface, and indeed felt his own do likewise. "I had not been ready to say this, but at this point I know it was only selfishness and fear that held me back. I understood why you did what you did long before I left, and I think I even managed to forgive you then too, but I was too afraid to lose the protection I gained from blaming you to admit it, even to myself. I was too afraid to tell you that I loved you as a father and that I forgave you, because it would mean that I agreed and then I would have been responsible for my own actions, without the excuse of blaming you." Harry sighed, pushing back his own tears even as he watched Dumbledore's flowing down his cheeks from his still closed eyes. Harry stood from the chair and moved so he was standing over Dumbledore's prone form. "Of all the things you gave me, it has always been your trust and love that I have treasured most. Someday, Grandpa, I hope I can join you in your next great adventure, and we can once more stand together." Harry leaned down and kissed Dumbledore's brow moving back to gaze into his now open eyes, which glistened almost merrily even through the sheen of tears.
Dumbledore reached over with shaking hands taking his wrist in one and placing something warm in Harry's palm with the other. "Thank you, my son. I have needed that." A fresh wave of tears escaped his eyes as he released Harry and settled his arms back upon the bed. As Harry gazed down at him, failing at last to stop his own tears from flowing, Dumbledore closed his eyes and breathed out his last.
Carefully wiping away Dumbledore's tears Harry stepped back and glanced down at what Dumbledore had given him. It was the HeartStone, much like a WardStone it was designed as an anchor for a great many spells, HeartStones were special as they were used in medical facilities to anchor spells that are needed to sustain life in those whose bodies or magic could no longer do it for them.
Madame Pomfrey spoke up behind him, he hadn't even noticed she had arrived, "He said you would come; he had faith that you would, even when we doubted it. You were the reason he held on so long." She paused a moment, gathering herself. "It does me good to see you two reconciling, even if it took so many years."