Hulk's Rules of Character (from r/movies)
1) The Hulk & Bruce Banner are absolutely different people. Unrelated entities that have the misfortune of existing in a binary state where only one can be present at a time via that body. Each has their own mind, passions, peeves, etc. The Hulk will often act in defense of Banner, but only because it knows it needs Banner to exist.
2) They don't like each other even remotely. Banner is appalled by what the Hulk has done, the destruction to innocent lives, etc. The Hulk is disgusted by Banner's lack of personal fortitude.
3) The Hulk lives in the moment. Over the years, in the comics, he's gone from cave-man ook-ook stupid to normal intelligence. Depends on the writer. However, in general.. the Hulk only cares about what might be a threat (or a challenge at all) that's right in front of him. This is why he chases the Black Widow, he saw her as some kind of problem and Hulk only solves problems one way - smashing them. The few successes people have had "directing" the hulk's anger has really been by diverting his attention. Side note: the comic most of this movie was based off - Ultimates vol.1 - The way they defeat the alien invasion is by Cap telling the Hulk the aliens thought he was gay. This angers the Hulk, as nobody could dare doubt the heterosexual power of the Strongest There Is. Shortly there after, Hulk jumps into the alien fleet and begins bashing ships together. This was 'muted' in the movie when Cap just pointed at the aliens and said "hulk smash".
4) In the movie, when Banner shows up in NYC and turns into the Hulk, the only reason it worked was because Banner knew the Hulk would not let him die, nor would it let anything threaten Banner's survival in general. So really, it was simply a case of both Banner and Hulk's agreement of what must be done.
5) Barring REALLY damned rare circumstances, the Hulk cannot be split from Banner, nor can Banner be cured. Yes, it's happened a couple times but those have involved top-tier cosmic powers. Ultimate Hulk (the version of The Hulk that is in Ultimates story) has never been divided from Banner.