We are not fathers by virtue of having the priesthood. Church government necessarily works differently than home government. You have a different kind of responsibility as a parent. A parent’s responsibility is vastly broader than a priesthood leaders.
Thus we need to stop reading these verses as being about how to be a father, when they plainly declare they are about priesthood leadership.
D&C 121:41 No power or influence can or ought to be maintained by virtue of the priesthood, only by persuasion, by long-suffering, by gentleness and meekness, and by love unfeigned;
42 By kindness, and pure knowledge, which shall greatly enlarge the soul without hypocrisy, and without guile—
43 Reproving betimes with sharpness, when moved upon by the Holy Ghost; and then showing forth afterwards an increase of love toward him whom thou hast reproved, lest he esteem thee to be his enemy;
44 That he may know that thy faithfulness is stronger than the cords of death.
Now this speaks as plain as day about power or influence by virtue of the priesthood. It does not say it is directed to fathers. There are scriptures directed to fathers and they say they are directed to fathers, such as those found in D&C 93. The Lord can tell the two apart and say what he means.
When we think that we can only reprove our children when the Holy Ghost tells us to, I simply don’t know what can be done for us. We are then unprofitable servants who need to be commanded in all things.
We are to train up our children in the way they should go. That will require reproof when they are coloring on the walls or hurting each other or lying or teasing or disobeying or any number of other things without the Holy Ghost needing to tell us so.
These are not verses about family. If they were, then yes, indeed, the Holy Ghost really would tell us every time a child needed to be reproved with sharpness.
But they aren’t, and he doesn’t. But if they were, then he would. Which would leave the poor nonmembers in a lurch because they would never know when to reprove a child, not having the gift of the Holy Ghost.