I think the rebel government idea could be done by unhappy Dwarves conspiring together to developing their own small entity groups that kind of represent "the rebellion" (like secret cult entities Toady has talked about making). There'd need to be long periods of persistent unrest depending on Dwarves personalities before they'd consider rebelling, maybe a counter like for artefacts, or it'd be a lot to track. But yeah, they could form an additional entity and try to overthrow the fort. Maybe not even violently right away, like instead they make ridiculing poems about the noble they blame for their conditions, build embarrassing statues, make agreements with guilds or religions or convert individuals to their cause. They create a history to fill in the feelings of the new entity so there's all this content it creates.
Actually a better way to do it would be to have it so that popular dwarves with lots of friends automatically create their own factions, provided they are not themselves nobles and these factions are either happy or unhappy. These factions always stand for election if their leader has no position already and unless there are no factions in your fort it is the faction with the most members that wins the election. Faction leaders recruit people into their faction if they are non-faction members but if the faction leader dies the faction member with the most in-faction friends takes over and relations with that faction worsen if the former leader did not die a natural death from old age (same to a lesser degree with all unnatural deaths of faction members).
Faction leaders contact nobles and by this means they periodically make demands to the player, based upon the personal likes/dislikes of the faction leader and their friends. They function rather like mandates in that they have a deadline and if the demand is not completed within the deadline it hurts relations, while if it is carried out swiftly relations are improved. A factions happiness cannot rise above the average personal happiness of it's members but importantly it can fall below.
Appointing faction members to noble positions makes the faction happy while dismissing members from noble positions makes them angry, more angry than appointing them to the office in the first place (squad leadership counts as an office). Nobles that are personally happy are disinclined to form factions or join them but will maintain faction loyalties from before they were appointed.
And maybe they still work for a while but then they refuse to work when their new entity overpowers their old one, but if they're still mostly cowards they might not start anything unless guards hassle them to get back to work and then they get sick of it. If they dropped their ruling civ tag entirely and kill the nobles and loyalists their new entity should be added to the playable list too. Then you can reclaim the fort playing the rebels but they need to fight off the old civilization, and maybe they get used to killing nobles so more nobles back their demands than before.
You should not be able to play the rebels any more than you should be able to play as the goblins that invaded your fortress! Dwarf Fortress is supposed to be a rogue-like, it is not supposed to be a game where if you lose you keep on playing as if nothing happened. You lost the game dammit, nobody is going to care about maintaining happiness if all that a revolution means is that the name of your site government changes and you have to come back in a fortnight's time.
The way that rebellion works goes back to how factions have a relations with your government. If a faction's relations go sufficiently low, say 0% then the faction goes into rebellion. Rebel faction members deactivate non-essential labours and are controlled by a basic AI that does certain things.
Rebels will always continue to do the following labours which are defined as essential. This ensures that a fort will not starve to death as a result of a rebellion.
Hauling.
Growing.
Butchery.
Milking.
Bee-keeping.
Hunting.
Cheese-making.
Animal Care.
Brewing.
Medical Jobs.
Herbalism.
Fishing.
Fish Cleaning.
Milling.
Rebel soldiers however refuse to do civilian work and automatically activate but refuse to follow orders. This keeps weaponry and armour in their hands as well as ensuring that they will be well trained. They cannot be dismissed from their squads and if the squad leader is a rebel then you cannot appoint new members to that squad. Empty slots within squads are liable to be filled by rebel faction members selected by the AI, giving priority to those who already have weapon skills and using a default uniform.
The rebel AI does not respect burrows but instead creates it's own secret burrow whenever a hostile entity or mega-beast enters the map, it avoids being on the same Z-Level outside/inside as the threat if it can. That is if the threat is outside particular level the rebels will flee the outside of that level and head either inside on that level or to a level below or above it.
During the rebellion, all rebel faction members actively try to recruit new members from among those who are not part of a rebelling faction, using their social skills. Unhappy dwarves and dwarves with little regard for law or authority are easy targets for recruitment, as are those who personally are on very good terms with the recruiter.
Rebellions do have a time-limit however, randomly set in advance. If the demands of the rebellion are not met before the end of the time-limit then things can escalate into either a violent or peaceful revolution. If members of the faction come to unnatural deaths during the time period then things have a chance of turning into a violent revolution before the time-limit is up. In a violent revolution the rebel squad members try to kill all loyalist forces and loyalist nobles or drive them out. In this form of revolution all civilian rebels that are able to grasp and walk are formed into squads when the violent revolution breaks out.
A violent revolution ends in victory for the government in a similar fashion to the way that sieges are ended, if the loyalist forces have an overwhelming advantage AND the rebel leader is dead then the squads disband and the rebellion is over, though the rebel faction will continue to exist under it's new leader. If the rebel leader is not dead then the rebel faction will leave the map and become bandits.
A peaceful revolution on the other hand has the rebels appoint a rebel alternative to a particular loyalist noble, they will then carry out actions to undermine his authority depending on profession, such as engraving the walls with insulting graffiti. Each of those actions has a government response, you can remove the graffiti with your loyalist stone detailers as their stone details carve it into the wall. When a peaceful revolution starts all loyalist nobles are given a authority score, they start with a score of 100% while the rebel alternative starts off with 0%. If the rebel alternative ends up with a high authority that your own noble then he automatically replaces your noble and cannot be replaced as long as he remains part of the rebelling faction.
A peaceful revolution has no time frame but can turn into a violent revolution if bad things keep happening to the rebel faction members. You can only end it by raising their faction happiness, which can be done by appointing members of a faction into offices; a wise player would appoint rebel members into offices whose holders are about to lose them due to authority erosion anyway.
If all nobles in your fortress are part of a faction and that faction goes into rebellion then you lose the game automatically and you lose the function of all nobles that are rebels.