Before you read on; please first read Emergency Evacuation Infrastructure. In this article I also discuss the sort of authority and chain-of-command in the colonies there could be.
Even before the actual launch of our first -manned or unmanned- mission,there should already be a CG. Its task at that moment is to facilitate everything,and have a central chain of command from the start to co-ordinate the launches,deliveries and builds.
The CG should have control over the Colonial Watch and the Colonial Militia. These will be the police department and the armed-forces of the colonies. Like I said in the EEI-article,we cannot just assume that Earth will always have a stabile climate when it comes to politics and war,so Space Colonies should have the power to defend itself,but perhaps also to intervene in wars on Earth? After all,one of the main goals here is to protect mankind from extinction,so it wouldn't be so stupid to do this,after all...WW3 will be a nuclear war which will exterminate a significant part of the Earth Society.
How does the democracy of the future work? Do we see ourselfs,even in 10,20,30 years, having to go to a voting station every once in a while and after that nothing? Or do we have to digitalize voting,just one-click on your phone,tablet or computer and you voted. But what for, do we vote for a Parliament, or do we vote for a referendum which enables the people to vote for each bill and doing so,adopting or rejecting new laws?