Well, in Zeta look at literally every single interaction Titans members have with colonists or colonies, as well as the way that they are cracking down on protest movements and generally passing around the oppression bat. In particular, I would note that this is essentially their mandate. It's the whole fuck over the Federation thing that gets the higher ups coming down on their asses.
In Unicorn, look at RE: 0096 Episode 6, timestamp 14:00 to about 15:50 (there are other spots if you care to look, but this was the first to come to mind). Now, there are several topics being discussed, but the important one for this discussion is that the early settlers were mainly beggars and political criminals, that they were an abandoned people. In being abandoned by both the Federation and, to some extent, God, these people then turned to Zeon. It's an attempt, mainly, to explain the fanaticism expressed in light of shit like the colony drop, but what's important here is that they were or at least strongly felt that they had been abandoned, as well as that the content of the early settlements was mainly the powerless and those out of favor with people in power. Those are not groups that get given political power, and at no point in Unicorn or any other series does it treat them like they have political power.
In Char's Counterattack, we see that the Federation elite do not consider space as a legitimate threat despite all evidence to the contrary, as they practically hand Char the keys to the kingdom.
In Gundam F91, we see that the Earth Federation leadership and military brass both are completely willing to allow the slaughter and conquering of colonies so long as the interest remains solely on the colonies themselves.
The exact political structure of the colonies is not, to my knowledge, specifically laid out, but it is clearly one in which spacenoids possess little, if any, political power and no real capacity to influence Earth Federation decisions. We see this in the original Gundam, where Side 7 was a military test site despite being inhabited and the civilians onboard the White Base were pretty low priority (and both Zeon and the Federation are clearly only allowing the independent Side to be independent because they directly benefit). We see this in Zeta, where the colonies are under the heel of the Titans with a level of approval from the Federation and a lot of apathy. We see this in Char's Counterattack, where the Earth Federation leadership is so wildly out of touch with space that they hand Char obscenely dangerous material. We see this in Unicorn, where the idea that spacenoids were supposed to have proper political representation is part of a scandal which could potentially topple Earth Federation administration. We see this in F91, where the colonies are generally neglected and treated like shit by the Federation.
