Rulership rightly understood has love at the centre, because God is the ultimate Ruler and God is Love. Rulership attained by coercive means is not true Rulership, it is Rulership corrupted by the Fall, motivated by greed, violence and the lust for power.
Agreed. God is a father, and all earhtly rule is modeling something of the fatherhood of God. In the home it is familial fathers, in the church it is ecclesiological fathers, and in the civic sphere it is city fathers. A man in authority may model God the father well or poorly, be a good father or a bad father, but in either case he is a father.