I love this idea, but I do strongly disagree with some aspects:

In general, once a family member is adopted or comes of age, you decide if he will take up a military or a diplomatic career, just like in real life. And once decided, you have to stick to it.
This was not the case in the ancient Roman Republic. Any young nobleman was expected to serve in no less than 10 campaigns if he wanted any kind of political career. Anyone who wanted to be a general would have to be elected to public office first.

The cursus honorum for a Roman noble looked like this: at age 20 or so the young man served with an army somewhere as a military tribune to get experience in war. At age 30 he entered could stand for election as quaestor and entered the senate. A few years after that he could stand for election as Tribune of the Plebs (if he was a plebeian) or as Aedile. (less influential) All these are essentially political functions, having nothing to do with the military.
At age 39 he could be elected as Praetor, the one-after highest official in Rome. The praetors were used for various political functions (lawcourts, foreign and domnestic offices) but were also sent to govern provinces after their term. This usually involved military commands.
At age 42 he could finally become one of the consuls, and the year after that would usually govern a province and lead armies if so inclined.
Most of these actual ages were only codified in the later republic, but the offices and the progression itself were in effect at the start of the game. (though in this time the actual consuls more often led the armies as wars were fought closer to Rome.)

Unfortunately for the Romans, there was no academy to train generals, which led to some spectucalarly incompetent field commanders, as well as some very good ones.

Anyway, to represent the real way wars were waged in the republic, the governor of a province would usually have to be the one to command armies. If he wants to fight an offensive war, he'd have to leave his province ungoverned. This would then cause much mumbling about "gloryseeking fools" back in Rome and complaints about misgovernment in the province itself, as well as being a royal pain in the backside for the player.

A more fun way to represent elements of this would be to send young family members back to Rome at the appropriate ages to stand for office for a year, if at all viable. The ages for consul and praetor are a bit too close for comfort, but say going at age 30 to enter the senate and at age 42 to become a consul could be done. Add aedile at 36 to taste. The more diplomatically inclined family members would also have to serve a couple of years with an army at age 20, before being allowed to go back to more peaceful pursuits.