So, what have you got for us, ideawise?
Domain Scores
A domain score which would track the strength of your domain (compared to other relevant ones) - this will determine the chance of success for winning an open conflict with a rival, and can be increased (or an opponent's can be decreased) through missions like recruiting mercenaries, diplomatic undermining, acts of sabotage, etc. It also means the domain can defend against attacks on it's own rating by way of counter-missions - stop the assassin, catch the spy, crush the resistance cell, etc. If the domain score margins are too close for a decisive victory, players can design their own missions to get the edge (we could either let DMs determine the domain score value of such actions, or have a table with entries like "Posion an army's supplies: -5 domain score" or whatever.
If you wanted a bigger dichotomy between war and peace, you could have two domain scores: Civil Score and Military Score, or something like that. Too low on the civil score means peasant rebellions and rioting (which would also adversely affect Military Score) - this opens the campaign up to subterfuge missions to incite uprisings in the enemy capitol or strengthen a local resistance group or something. Taxes would likely be rolled into that in an abstracted way: instead of worrying about gold, taxes are represented by modifying domain scores (higher taxes means a better Military Score but weaker Civil Score if all the money is used to raise an army, or vice versa if the money is spent on hospitals and schools and whatnot. Either way, more people means a higher overall Domain Score because of tax wealth).
Military
I have already shared my rules for running mass combat on these forums, but if players aren't into it you could just compare opposing Military Scores and devise some formula for figuring a victor (and a table of consequences for military wins/losses). Military missions can also be devised (gathering superweapon parts, or befriending a dragon or whatever), which allow players to quest while still seeing a direct benefit to their realm for doing so.
Diplomacy
I guess a subsystem tracking faction feelings towards one another and likelihood of helping/hindering would have to be included somewhere, though the DM could just as easily simplify this with "the Barbarian Nations don't like you so they won't help when called upon, and the Eastward Counties are friendly but Count Figaro has betrayed you in the past and might again, etc." I'd nix the nitty-gritty stuff like trade goods, immigration, cultural influence and all that other stuff from a Civilization game... it's too much.
Spending
Players can influence their domain score by spending (military or civil), but they should also trust that their underlings know where to put money. Can potentially spin off missions like capturing an embezzling defector, or the new hospital is out of medicine and needs a trade path cleared, or the swords you bought for your army are brittle and you need restitution for being swindled, etc. Basically, sometimes the group spends on their domain but a hiccup means there's a problem to solve before the bonus is applied to their Domain Score. Could also include long-term spending that needs further investment - building a fort, for example, takes months and would probably spawn resource gathering missions or defend the build site missions.
Event
Big old table of random, civilization-scale events. Epidemics, freak droughts, visit by a major religious figure, etc.
Anywhoo, just a starting basis really. I'm thinking in general, you've got maybe three or four numbers to track and then a bunch of missions to generate. As leaders, some missions can be delegated to underlings, so it'll probably need a brief formula to determine the success of an underling at any given mission.