Cobb is in reality at the end of the movie

Cobb is a dude who became mentally unbalanced, following the loss of his wife - either she slept with another dude, or she died, or she simply left him, because he kept failing to bring home the Oscar.

He lives in a delusional reality he concocted inside his disturbed mind, where he's an agent who can enter other people's minds, via a rubber cord coming out of a suitcase, that he straps around his arm. The guilt he experiences from being unable to prevent the loss of his wife, manifests as paranoia - government agents and occult organizations assassins out there tryin to get him.

The cold baths that his psychiatrists administer him, to take him out of the episodic deliriums he sinks into, he sees them as ways of getting out of "dream levels".
His father finally finds the right psychotherapist for him, in the person of what Cobbs sees as "student architect", who knows how to build "labyrinths". Like you need to be an architect, to build a labyrinth...
Ariadne helps him in one last "heist", where she incidentally helps him throw Mal, the very wife he loves, out the window.
Then he wakes up in the "real world", like from a terrible "dream", and no more occult organization assassins tryin to get him, no more government agents chasin him around the world.

The poor guy comes home to his children, and spins a shtoopid top, that he was unable to spin before throughout the movie.

The spinning top maintains balance. So is the subject's mind maintaining balance. Cobb's pop thanks the psychotherapist for a job well done. But Nolan cut that part from the movie, he needs monies, and nobody would see this movie twice, if they'd figure what da faq is it about.

Inception is a remake of Hitchcock's Vertigo.

There's multiple different theories out there that can counter yours. I mean MANY. So sorry, this doesn't really prove anything

The children do not have their backs turned because he is dreaming. They have their backs turned because Cobb is still in touch with reality enough to realize that if he looks at their faces, he will fall for the delusion. That's why when he is with Mal at the very deepest "dream layer" near the end of the film, he shields his eyes from looking at his children...which he does by the end of the film, because he ends up believing he is in reality.

The fact Cobb used the totem as a mere placeholder is evidence that from the beginning he already had placed faith in an element of reality that was merely within his giant dream, which is why he ended up looking at his children's faces.

Someone else talked about the top wobbling back and forth. I hate to break it to them and anyone else, but the wobbling is not ample evidence that it ends up toppling over. It merely comforts the audience so they won't have to ask anymore questions. The shot does not remain on the top long enough to show us that the top's wobbling becomes increasingly more drastic and intense as it would before toppling. We simply see it begin to wobble.