Didn't say much about Rome faction...
I hope the Republic dynamics are a bit more interesting, there wasn't much too them in Rome 1. Houses should pretty much be under control of the senate, like you are playing the head of it and given assignments like govern X province, build up an army and conquer province Y (and you are given some gold and troops to get you going). If you succeed you amass popularity and wealth, if you fail you lose it. With popularity you can win votes to control republic offices, with wealth you can do stuff like build up your palace for prestige (popularity & offices), invest in business ventures, or fund a household retinue. Then if your house becomes powerful enough to come close to dominating the Republic, it could spark a civil war event.