The Azog storyline isn't really in The Hobbit
at all but it was 'written' for various appendices and for other outline/background work that goes into the general mix for the various components of The History of Middle Earth as edited by Christopher Tolkien before and after The Silmarillion
was assembled. The 'official' history for TH was put in when the book was revised once LotR was going to be published to make the two fit together more consistently with the additional material that gets covered in The Shadow of the Past and The Council of Elrond.
In context with canon (so the book) Azog is actually killed by Thorin's father Thrain in the battle as flashbacked to so he's long gone for TH timeline, BUT Azog's son, Bolg is the leader of the Northern orcs who does come into TH much later on for the final culminating Battle in Erebor. Basically he exploits the power vacuum left by the death of the Great Goblin (no relation to Azog at all) and musters the orcs to take vengeance for the ancient hostility between Durin's Clan and the Misty Mountain orcs and also grab some dragon gold of course.
The dwarves, Bilbo and Gandalf do fight with wargs more than goblins after briefly escaping the mountains (the Out of the Frying Pan chapter) and get rescued by the Eagles but no heroic fighting at all takes place.
And you're quite right -Thorin also doesn't like that Gandalf's got his father's map and key too much either and is highly skeptical of his motives in seeking them out, but again this takes place before The Unexpected Party and is skipped on by and large. In the subsequent writings Gandalf explains by saying that when he found Thrain the poor dwarfie had completely lost his marbles and didn't even tell Gandalf his name or his son's so that was why he hadn't come to find Thorin years earlier . Perhaps this will covered more in film 2 or 3 depending on how soon they're going to bring in the Dol Guldur sections as that is nearly all 'not' part of TH, except by omission under the heading of 'what Gandalf got up to while the Dwarves and Bilbo got through Mirkwood'