Alright, to start off: I fully realize just how big a deal it would be to implement something like that. It probably would be too much for even an expansion. That said, I want to put it out there, if for no other reason than it being fun to talk about.
The basic concept: independant planets are political entities that can be talked to, traded with on a limited basis, and favours bought or beaten out of them. They'd also have the potential for acting as less involved versions of minor sims, to the point of fielding small planetary militaries and their own wheeling and dealing.
This would apply to both your own and to AI civilisations. When you start rolling over enemy territory, planetary governors could end up asking not to be hit in exchange for not putting up a fight. If you wanted to give a competitor something too think about, you could bribe a few of his planets into seperating into a new (or hostile) civilisation. You could procure business deals (small economic treaties) from a planetary governor (your own, and others) and these would be additional bargaining chips at your disposal... unless you want the money for yourself.
Your own planets would have their own governors... properly set up, they could manage their own freighters and scouting parties, and possibly even warships. They could even be doing some wheeling and dealing on their own, buying business deals from other factions for themselves. Of course, it also brings a whole new direction to domestic politics: namely, the pain in the ass that planetary governors can be if they want something.
Planetary governors always want more power for themselves. This means they'll ask for ships, money, or influence assigned to them. They might really help you out when using these things, but you lose control... and they could end up using it against you.
How these governors would act would be largely dependant on the political system you're using. A dictatorship really doesn't have to deal with governors... any of your hand picked governors would be (at least outwardly) loyal, and wouldn't put up much of a fuss. Their position depends on your good graces. A republic starts seeing more independantly minded governors. Once you get into more advanced forms of governments, you're getting some pretty independant colonies, and you'll have to keep an eye on things.
So, what do you do when things are starting to smell funny? You always have the option of kicking a governor around. Seize their ships, seize their treasury, kick them out of office and put a more friendly governor in their place (or run a byelection, if you choose). Stick federally run ships and transports near the planet in question as a threat. You've got plenty of options... and how the governor reacts depends on their loyalty, how powerful they are, your political system, and how much the population likes you. They might refuse to surrender their ships if the population is in favour of telling the feds to #$&* off, or even take such threats and rhetoric as a reason to seperate and take as many people with them as they can.