If I think of a goal of parenthood, Psalm 112 sums it up perfectly:
Hallelujah! Happy is the man who fears the LORD, taking great delight in His commands.
His descendants will be powerful in the land; the generation of the upright will be blessed.
This psalm explains the goal of a multigenerational legacy. God desires that parents will fear the LORD in every way. They will not only obey His commands, but they will enjoy doing so because His commands are not burdensome (1 John 5:3).
For the parent that accomplishes this, the desire is that his or her children will live mighty lives marked distinctly by holiness.
This destiny will not happen by accident.