I always assumed that the member-worlds (or larger organizations) of the GTVA (and the GTA before it) had traded control of external policy in exchange for military protection, economic benefits (free trade), and possibly assurances that if things for them go totally to hell, whether economically, socially, or politically, somebody will be there to help them clean up the mess.
Also, a statement made by Command during "Mystery of the Trinity" leads one to believe the GTVA is more then just the alliance it calls itself. "Your designation is incorrect, Roemig. Your ship defected to the NTF ten days ago. You have been stripped of your rank and citizenship in the GTVA. Surrender the Trinity, or be destroyed." (Emphasis mine.)
I'm going to hazard a guess and say the GTVA is comparable to the Consortium of Civilized Worlds from Rifts. It is a collection of worlds that have surrendered control of their external policy in exchange for economic benefits and military protection. There is a minimum standard that a member-world or member-alliance of the GTVA must meet in terms of the rights of its citizens (though not necessarily the form of government: if a military dictatorship can give its citizens basic rights and manage to not infringe on them constantly, it could in theory join), basic things such as trial by jury and such. If a world does not meet the minimum standards, it is not accepted. If it falls below the minimum standard, it is kicked out.
Dual citizenship in both the GTVA and the appropriate member-world or member-alliance is automatically granted. In cases where the laws of the two conflict, the laws of the GTVA take precedence. Those who serve the GTVA directly, as part of the armed forces or in some other capacity, are considered to be citizens of the GTVA and the GTVA only, and may not be held accountable to any laws but those of the GTVA. Civilians not working for the GTVA are subject to both GTVA law and those of wherever they happen to be at the moment.
Members of the GTVA would appear to not be allowed to maintain their own military forces, or at least ones of significant size. The NTF, after all, was composed of mainly the GTVA 6th Fleet and ships recovered and reconditioned from the boneyard in Polaris.