I have a friend who won't say the Fatima prayer during the rosary. He believes it invalidates the rosary based on the anathema attached to anyone who changes the rosary. If that isn't odd enough, he also has the priest at his church not using the prayer during public rosary. Is there any validity to his reason?
As someone has already written: the Rosary is not a Sacrament, so issues of validity do not apply.
The Dominican Rosary, the one most diffused throughout Christendom, consists in praying once the Lord's Prayer and ten times the Angelical Salutation for each of the fifteen Mysteries
whilst meditating upon these same Mysteries, which are customarily divided into three: Joyous, Dolorous and Glorious Mysteries. This is the definition given in the Roman Breviary in the Second Nocturn lessons for the Office of the Solemnity of the Most Holy Rosary of the Blessed Virgin Mary.
In order to gain the indulgences in the Raccolta, this is the absolute requirement, except that you may divide the decades of the Holy Rosary throughout the day as long as you recite five decades within that same day.
The addition of the Minor Doxology, the antiphon
Salve Regina, &c., were added later, under the influence of the Dominican structure of the Divine Office. From the beginning, the Holy Rosary was considered to be the Psalter of Jesus and Mary, so that the 150 Angelic Salutations correspond to the 150 Psalms in the Psalter of King David which form the nucleus of the Divine Office recited by canonical obligation by clergymen, professed Religious, Canons, &c. Later, the Apostolic Symbol and the preliminary
Pater and three-fold
Ave were added, and the Fatima Prayer was added in the 20th century. Adding these and other prayers do not take away from the Rosary; they are supposed to enhance one's attention and affection whilst continuing or concluding the Rosary.
Again, the essence of the recitation of the Holy Rosary is the praying of the Lord's Prayer and the Angelic Salutation
together with meditation on the Rosary Mysteries.
I have posted some material that may be helpful:
http://www.cathinfo.com/catholic.php/Daily-Rosary