We're not mod junkies! *grin*
But seriously..
Vanilla indeed means out of the box no mods or addons. Only the the latest patch applied.
As for combining AA2 and AO its quite easy. First install AA2 in its default location, and then install AO to the same location. I cant remember, but i would'nt be surprised if it asks you if you would like to do that.
The last few times we have only played maps that are vanilla, the problem that you could'nt join was because you werent patched to the same version.
As for the addons from bohemia themselves. A light free version of the last two (BAF and those private contractors) comes in the patches. So with just AA2 and AO patched to the latest, we can all rock together no problem.