Nope, Auriel wants his power back from Nirn; Alduin wants to destroy the world so he can create the next one (which he will then destroy, to make the one after that...), and Akatosh likes Nirn just the way it is.
And yes, they're all the Dragon God of Time.
It seems that Akaduin-El (made-up name for all three of the above together) IS time, and any conflict of interests that appears to exist between the three of them is just the complications of personifying a concept that is not concerned with the fate of mortals. Generally, Auriel wants things the way they used to be, Akatosh is the mover of the group, doing things in the present to prepare for Alduin, who wants to move on to the future (or at least continue the cycle, which is progress). Now I am not saying that these three are actually the past, the future, and the present, but I am saying that the actions taken by one god can appear to conflict to mortals, when in reality said actions are simply the result of concepts brushing past one another. It seems as though the avatars of gods (the walking, talking things that people like to worship) are a way for concepts to promote themselves in a way that is more fantastic and, debatably, more interesting than the actual world. It would make sense for different peoples to have different views of a god's actions. Some elves want to be free of the limits of the mortal plane, so they identify with the time before. The Nords, for the most part, are not okay with the world ending, so they dread the time to come. The Imperials aren't thinking of either of those things, so they enjoy the time they have.
Simplified (and leaves out the role of mortals), but I think its about right. Lore Gods correct me if I am wrong about something.
So yes, Alduin is Akatosh.