>>723953469
Several things happened between the One Year War and Zeta, mainly the remnants of Zeon forces attempted several terrorist attacks on Earth and other colonies and killed thousands of innocent people. To combat the remnants of Zeon, the Titans were formed. It just so happens that the Titans have their own political agenda: they're extremist anti-spacenoids who are willing to genocide entire colonies if they so much as say "hey, the Federation's taxes are too high." The Federation doesn't exactly know about the Titan's actions, but the Titans can do whatever the fuck they want as long as they claim it's for Earth's security.
Since the Federation was slowly but inexorably becoming a totalitarian, corrupt government, the AEUG was formed. The Anti Earth Union Group is a paramilitary group with ties to Anaheim Electronics that seeks to reform the Federation and stop them from becoming a totalitarian corrupt government. Char joins them because they have a common enemy (the current Federation) and if they succeed they could actually create a more stable government that benefits both earthnoids and spacenoids. By this point in time Char has actually mellowed quite a bit and has a more nuanced look about the war. At the beginning of Zeta he actually believes the Federation can be reformed and the AEUG can make a change.
Oh, and Kamille joins the AEUG because he despises the Titans and he distrusts the Federation.
As for his "disguise", Kamille knows he's Char. He's even credited as "Char" in the credits. Most of the crew are pretending not to know who he is.