Here's an idea:
Each civ has an "Old Palace" (name should be different for each civ, like "Palace of the Ancestors", "Whitehall", "Versailles", etc) that gives a small maintenance bonus, defense bonus, and quite a bit of culture.
When the palace is moved, either deliberately, or by conquest, the old palace is built in the city that used to have the palace. But this only happens once per civ.
When you conquer a former capital, with the old palace national wonder, you also get a "subjugated bureaucracy (or administration, etc)" building, it generates unhappiness, unhealthiness, a maintenance penalty, and generates culture for the old civ! After several turns (a decade, basically) it is replaced with a "cooperative bureaucracy" generates a minimal amount of unhappiness. Later on (a generation) it is replace with a "district administration" which generates some happiness, gives a maintenance bonus, culture, and 1 mana.
So basically, when you capture a former capital, at first, it's a liability, but gradually, it transitions to become a regional capital.
A few scenarios, using (for sake of familiarity) england, france, and spain.
1) england captures paris. instantly, the french palace becomes "versailles", and about 100 turns later, paris starting generating 1 mana (umm... is "too many vowels" a type of mana?) meanwhile, the french built a new palace in nice. eventually, england takes that from france too, but no old palace or administration is built, since they already exist.
2) france moves their palace from paris to rousillon. instantly, versailles is built in paris. a few years later, spain captures rousillon, but since versailles has already been built, no old palace or administration is built in rousillon. eventually, spain drags england into the war, and the redcoats march into paris. they keep the old palace, and add an adminstration to it. England Prevails!
3) when england marched into paris, they decided the eiffel tower violated their building codes, so they raze the entire city. france rebuilds their palace is nice, just in time for it to be nicely conquered, and transformed into versailles + admin. Then france reconquers nice, and they behead the bureaucrats who had cooperated with the enemy.
4) england captures paris, gets old palace + admin. france gets assistance from spain. spain captures paris, and razes it to the ground. england captures nice, and gets a brand new old palace + admin. maybe.