In which way has this unity been violated in the course of history?

Very early on there were already splits in this one and only church of God, which the Apostle (St. Paul) criticizes severely; in later centuries, more dramatic differences developed and not unimportant sections of the community separated from the full community of the Catholic Church, occasionally not without guilt of people on both sides“ (UR 3).
Among the communities which developed after the separation from the Catholic Church are the “Protestants”.

”But those who have now been born into such communities and who are filled with faith in Christ, cannot be blamed for the separation, and the Catholic Church meets them with brotherly respect and love. ...they are justified through their belief in Baptism and are part of the body of Christ, and therefore they deserve the honorable name of Christians, and the Catholic Church rightly recognizes them as brothers in Christ.” (UR 3).

Furthermore, beyond the visible boundaries of the Catholic Church, “many elements of sanctification and of truth are found “(LG 8): “the written word of God, the life of grace, faith, hope and love, and other internal gifts of the Holy Spirit and visible elements” (UR 3). The Spirit of Christ uses these churches and the church communities as a means towards salvation. Their strength results from the fulfillment of the grace and truth, which Christ has entrusted to the Catholic Church. All these goods come from Christ, lead to Him and on their own accord, strive towards Catholic unity (cf. LG 2-3).