Instead of a sudden, "Blah Blah planet has revolted and joined up with Blah Blah", why not make it better?
When your enemies influence around your planet is 4x that of your planets influence production (or when the little revolt sign shows up), a few squares on that planet should turn red and have a transparent revolt sign over them.
That red tile means that the revolting part of your planets population has control of it.
If you don't do anything about it, the revolters territory will grow on that planet.
When all the tiles become revolt tiles, the planet will become property of the enemy.
Now for the interesting stuff...
If one of your improvements become a revolt tile, that improvement will no longer function.
(This makes long term affects of doing nothing disasterious)
You can do two things to stop the revolt...
1) build a happy center or influence improvement.
2) send troops in from another planet to help kill off the rebellion. (if you do this, the enemy will declare war on you)
Also, the secret police center would now slow rebellions down instead of just give happiness bonuses.
Who thinks this would work better, be more interesting, or just be plain cool?