Paul White explains in this video that just as God commanded Abraham to keep the ways of the Lord, fathers are likewise to do the same today. They are to instruct and demonstrate what the ways of the Lord are. They aren't just rules -- they are the ways of God and who He is. The commands of God are just as relevant today as they were back then.
1 John 3:1 (NKJV) - "Behold what manner of love the Father has bestowed on us, that we should be called children of God! Therefore the world does not know us, because it did not know Him."
So Genesis 18 19, God speaks to Abraham and he says, speaking of Abraham, for I have chosen him that He may command his children and his household after him to keep the way of the Lord by doing righteousness and justice so that the Lord may bring to Abraham what he has promised him." So how does this apply to modern fathers and fathers in every generation? It's our job to do what Abraham did. It's very simple. Command his children and his household after him to keep the way of the Lord. To instruct, not only verbally, but by way of example, what the way of the Lord is.
Again, God reveals Himself throughout the Scriptures. In Deuteronomy, it is teaching the commandments of God. These things are not just rules. They are the ways of the Lord. When we understand God's law and we understand God's revelation, we're not just learning rules.
We're learning the ways of the Lord. How this God is. What He is. How He thinks and acts and, for lack of a better word, responds to situations. We're learning of God.
So it was Abraham's job to, yes, command and instruct with the rules, but also do so in such a way that his family and his household learned about God, the nature and the character of God.