I don't think it's like that. This organization existed for decades, so it is clearly establishment. The hat guys should have no interest in major changes in the ghoul world.
Kanou said he and Aogiri have the same goal when he joined Aogiri, so if he is a member of the organization, Aogiri would be a branch of it. But Yoshimura fears that the organization could harm his child that seems to be the head of Aogiri. Why would he fear that they would harm his child if Aogiri were a branch of the organization?
It's likely it's the other way around. IIRC, Kanou said that "someone" placed a cage around the world, and that the power of the one-eyed ghoul is needed to break that cage. At first, I thought he meant CCG's higher-ups, but what if he really meant the hat guys? That would mean Aogiri is trying to fight against the organization.
These hat guys seem to dress similar to the doves... Is there some connection between CCG and the organization? Both organizations are establishment.
The half-ghoul project is strange. Officially, CCG never started this project for ethical reasons. Nevertheless, it was a CCG project, since CCG built the underground facility (but CCG disguised the ownership). Why would CCG be interested in creating artifical ghouls? That doesn't make sense. On top of that facility is a mansion owned by Yasuhisa. If he was involved in CCG's research, he should have been under CCG's protection. But some random ghoul killed him and his wife. Amon's conclusion is that CCG erased him. For what reason? Did someone put a stop to the project and ordered cleanup?
Then, Kanou, a former CCG physician, takes over the facility and continues the research. He successfully creates at least three artificial ghouls: Kaneki and the Yasuhisa twins. During the raid of his lab, Kanou and Aogiri join forces. Kanou should be somewhere else now, creating lots of artificial ghouls.
I'm still waiting for Touka and Kaneki to become a couple. I miss Touka bossing Kaneki around.
I think that Touka is also lonely. She clearly misses Kaneki. When she was at Kamii, she was thinking about Kaneki all the time. The only other person Touka is relatively close to is Yoriko, but Touka has to hide from her who she really is.
Touka's family is complicated. Arata was caught by Shinohara and Mado (it's ironic that in the end, Touka unknowingly killed one of the investigators responsible for her father's fate) and turned into one of CCG's experimental subjects. (Shinohara is running around with the quinque "Arata", that armor. CCG is still "improving" it.) The fate of Hikari, Touka's mother, is not so clear. However, Hikari looks a lot like Yomo's sister and Arata looks a lot like the guy that apologized to Yomo that he couldn't protect Yomo's sister. That would mean that Yomo is Touka's uncle (I don't think Touka knows) and that Arima killed Touka's mother.
And the brother is going around killing ghoul investigators.
It seems to be a family trait that each family member goes berserk at one point in time. Yomo, Touka and Ayato are examples.