At its core, the whole problem comes down to populists. A populist senate makes it almost impossible to declare war, even though the missions you get want you to declare war.
I suggest again that you read the Unofficial Strategy Guide for republics; doing so and understanding it will really help with managing populists. In short, you want as few characters to become populists as possible, so every few game years just go through the character browser and arrange the character list in order of ambitions. Go through the list and assign the titles that those characters want. If there are any characters with a little brown box where their titles normally would be, it means that they want a job - give them a minor title as well to keep them happy. It is a little bit of micromanagement, but you really only need to do it every now and then (I've set the game to pause whenever I get a new ruler, so I just do it whenever there's an election).
Have a look at the government window. Hover your cursor over the number of populists (shown under the portrait of the populist faction leader) and take note of what the faction's attraction is like, and what is contributing to that attraction. The main culprits are:
- having no omen invoked
- not having buildings built
- not having trade routes set up
- having a populist faction leader with a high charisma stat (I imprison any populist leader with >3 or so charisma).
By following those guidelines, you should rarely get more than 20 populists in the senate at any one time. If you want to get rid of your populists now, then encourage a non-populist consul and let the populists rise in revolt. Defeat them in the ensuing civil war and follow the above suggestions to keep them down
