What is the i. scriptural basis of the Rosary of Liberation; and ii.the Vatican’s position on it?
To be honest, I had never heard of it until your question. The Rosary devotion itself has evolved over time and even recently had a new set Mysteries approved for public devotion (the Luminous Mysteries). The Chaplet of Divine Mercy is also another devotion that uses traditional rosary beads. So its not out of the question that a devotion could begin that uses rosary beads or an alternate set of Mysteries.
According the the blog Women of Grace the book that this private devotion is based on “has received two imprimaturs stating that nothing in the book is contrary to the Faith. In addition, the authors, Regis and Maisa Castro, received glowing letters of support from Rev. Gilberto Pereira Lopes, now Archbishop Emeritus of the Diocese of Campinas, Brazil, and Evarist Pinto, Archbishop of Karachi, Pakistan.”
The Vatican normally does not take positions on such things, it leaves them to the local levels. The Bishops who have reviewed it have, apparently, found nothing in this devotion that is contrary to the faith so I see no harm if someone chooses to pray using this devotion.