Even within man there is a hierarchy and order of peace (and to some extent this order is shared between the two cities--but only to some extent). We share with the animals the "peace" of avoiding pain. However, we do not stop there, as humans we add at least a rational element, if not also Divine grace as a guiding hand to our pursuit of peace. This latter of course applies only to Christians, and is the means by which we walk by faith in obedience in this world. This obedience is likewise taught by God, and includes the "two chief commandments": love God and love your neighbor. It is in this love that our peace is found both within ourselves and with other men. This responsibility to love begins in the home and includes all whom we have direct influence over.
This peace of the household is the only peace that God intended according to "what nature prescribes." Slavery, which has been added to this situation, is a result of sin and violence. And by this, Augustine means directly a result of sin--if you are a slave, it is either because you have sinned, or because (if you're a believer) being a slave is going to keep you from committing a worse sin. Again, this is not to say that slavery is a good thing, it is simply a reality of the world which must be acknowledged and accounted for as we try to love God and love our neighbor.
Even in the home we see the principle that disobedience and unrest is "disciplined by words or whipping, or other kind of punishment lawful and licit in human society." This is for the good of the wrongdoer to restore him,
For there is no more benevolence and helpfulness in bringing about the loss of a greater good than there is innocence and compassion in allowing the culprit to go from bad to worse. It is the duty of a blameless person not just to do no wrong, but to keep others from wrongdoing and to punish it when done, so that the one punished may be improved by the experience and others be warned by the example.This peace in the home, in turn, is connected to the peace of the larger society. This is why society has laws concerning what goes on in the home--the two cannot be disconnected.