Generally no. As a father, I have dominion over my family. Still, if my kids were to do something illegal in public or to someone from a different family, the local authorities would have dominion over justice.

However, for justice (and many other things like education/moral formation) within my family, I can exclude a father from another family from intervening in our affairs or, more importantly, excluding the state from teaching things I disapprove of. So, in that sense, I have a monopoly in my position of authority in the family.

This nuance is articulated as subsidiarity in the Catholic tradition: the principle that decisions should be made at the most local level possible, with higher authorities intervening only when necessary. The concept goes back to at least the 13th century with St. Thomas Aquinas’s Summa Theologica, but Pope Pius XI used it specifically in his papal encyclical Quadragesimo Anno, which is an important document in the history of Catholic Social Teaching.