The Shepards of Christ have a website www.sofc.org
Fr. Carter is a deceased Jesuit priest. I think he taught Theology in Ohio.
My mom is deeply involved in the Shepards of Christ. I have only see good fruit in her life. Their mission is to pray for priests, and promote the rosary. Mom is convinced the Rita Ring is an authentic visionary.
As far as the messages go, they seem pretty generic to me. However, the group is orthodox and faithful to the Church. They do seem to attract very prayerful and orthodox Catholics. In my judgement the messages may be more pious imagination; however, I have never seen anything contrary to the Faith.
I can't speak to the Church's position, but I believe they have imprimaturs on all their publications.