I also find this concept a bit iffy. Siring your own bloodline seems like an interesting mechanic, but it becomes rather uninteresting if all your sons are simply general, and all your daughters are bargaining chips; this may not at all be what Brad intends, but so far fathering children doesn't seem to have many advantages. I have an idea for a system in which family members will be crucial to maintaining your economy and inner diplomacy, as well as opening intersting options for outside influence. Of course, I am not a deisgner, which leaves me the luxury of raving madly about extravagant systems, but I'm glad to contribute to the development of Elemental, and I hope that the guys and gals at Stardock don't wear their eyes out reading my wall of text.
First of all, the sovreign's family won't be the only bloodline in his kingdom: tribal structures from the wasteland have survived and evolves into noble houses. Each kingdom will have several of these. The noble families will each have two attributes: number of family members, and prestige, both of which could be decided by the kingdom's own prestige (more on the role of family prestige later on). These families will be somewhat loyal to their reigning sovreign, but they will ultimately be independent entities.
Brad has already spoken about big empires needing to separate their cities into vassal empires in order to keep the economy manageable; this mechanic does not only add great depth to diplomacy and economy, but also faithfully recreates a primitive world with slow communication and transport. What I propose is to couple this system with the families. The system is as follows: when your economy starts getting muddled and your empire overstretched, you need to start giving cities some more autonomy. For this, you need to choose a noble to oversee that citie's production and tax collection. At this stage, you have two choices: first, you may assign a family member to govern the city; doing so has two great advantages: your family members have greater loyalty towards you (though it is not absolute, and can still be swayed by enemies through diplomacy or magic, as I have described here), and when a family member controlls a city, you get full returns from its production and taxes. However, if you run out of offspring (or if someone has assassinated them all), you will find yourself forced to appoint a member from one of the noble houses in your knigdom; however, the problem with doing so is that the noble houses can be manipulated by your enemies, and in addition will keep a percentage of the city's taxes and production for themselves. This system adds much greater value to your descendants, rather than having them simply be a deciding factor in succession.
I have already mentioned that the noble families could be manipulated, both by you and the other sovreigns, so let me explain how that would work. Simply, a noble family that has been assigned a city would behave as a minor side as far as diplomacy is concerned; this doesn't mean that they will act on their own like an AI, but rather that the usual diplomatic options will apply to them. This mean that a sovreign will have to keep his noble families in good relation, just as he would an AI empire. Ultimately, the families would be interested in money and prestige, and so a sovreign wishing to keep his nobles under control will have to pander to those need. Gifting them money is pretty straightforward, but granting prestige to a family might be more complicated, and could take several forms: for instance, placing a larger garrison in the vassal family's city, or marrying one of your daughters to vassal nobles. In addition, a noble family may be upset if it is assigned to a city with lower prestige than its own (which would force a sovreign to increase that city's prestige through the regular means). Under normal circumstances, a sovreign shouldn't have to work too much to maintain the familie's positive disposition. It only gets intersting when another empire starts to make some very attractive offers to the family. Doing so should certainly not be easy: an enemy empire would first have to infiltrate a spy or scout into the city, and create a situation favorable to befriending that family (just like one would do before proposing an alliance in Galciv2). After a fair amount of diplomatic effort, an empire can propose for a family to shift over to his side, through a gift of money and prestige; this would be done just like diplomacy in Galciv2, where you simply select your offer (marrying a daughter to the family, giving it more cities...) in exchange for the family's offer to shift to your side. This would enable the gaining of cities through diplomacy alone, creating a viable alternative to brutal conquest.
However, an enemy sovreign's children could not be manipulated in such a way, whence comes their significant advantage. Despite this, it may be intersting if they might also rebel against their progenitor under extreme circumstances, or when under a mind controlling spell. Imagine for instance a scenario where a sovreign's son tires of toiling for a king who will never die of old age, and decides to speed his succession by marching his loyal army into the capital.
Finally, this system may sound complicated, but its base is in fact rooted in existing mechanincs, such as the diplomacy system and the prestige mechanic. It would not only create greater value for family members, but also add depth to diplomacy and to empire management, not to mention that it would make the world feel more like a living thing, rather than a gameboard filled with mindless slaves (which is not always bad, but Elemental seems to be trying to be almost a simulation of a fantasy world).