Sunnis and Shi'a have been fighting for centuries, and it doesn't look like they're terribly interested in stopping soon. It was going on before Saddam and will likely continue for some time.
'Iranian agents' isn't quite the right way to look at it. It's 'Shi'a agents who happen to be Iranian' because religion drives politics there as much as, if not more than, nationality. It's natural for Iranian Shi'a to want a neighbor with a similar mindset. If they're stirring up the Iraqi hornet's nest to get it, however, that's a problem.
I don't know that all of Iran is bent on the destruction of Israel, even if Ahmadinejad has made his feelings well known. In fact, Ahmadinejad's very vocal stance on the matter (among other issues) is likely what's driving his popularity down. Most Iranians aren't too excited about making active enemies out of their neighbors after what happened in the Iran-Iraq war, nor do they want to take on the world with only Venezuela as their ally.