Politics 101 (the only guide you need)

1. DO NOT EVER... NEVER EVER... upgrade enemy generals (p.s. characters not of your dynasty are an enemy).
   1a. Upgrading skills/stats/perks also increases gravitas, most of the time, which will lower your political power.
2. Make them all generals, because even low gravitas character can/will influence political power.
   2a. Game Logic: if they're not over-seas, fighting wars, they're messing with your political power.
3. If the enemy dynasty (political group) has too many characters, sent them off to die in wars.
   3a. You'll take the hit for a military loss, since you're in charge, but this is good for the long game.
4. Retire/hire at least one high/mid gravitas generating character, who will act as a statesmen.
   4a. It helps with the long game and allows you to counter mistakes, like all-hands-on-board wars.

Note: The idea is to remove/minimize enemy influence while increasing your own, which also increases with military victories.
Notea: If you kill all members of a political/dynasty group at the start, it dies off for good; but will be replace eventually.
Noteab: Later on, killing all members of a political/dynasty just has a new member spawn; rebellion is the only fix.