Conflicts on power and wealth were what divided the monarchy and the church. The Church rose to dominant power in the West after the fall of the Roman empire in the 5th century. It expanded in the beginning of the 10th century as well as the secular kingdoms. Their peak of authority over all European Christians involved events like the Crusades and the Pope claimed the right to depose the Catholic kings of Western Europe, sometimes successful and sometimes not.
One example would be the Investiture controversy, where a dispute between the state and the church emerged in the mid-11th century and was resolved with the Concordat of Worms in 1122. It seemed to be a conflict of appointment of offices but it was actually a powerful struggle on who held the ultimate authority, the King or the Pope.
Another example would be the Magna Carta where the separation of the church and state can be found. Although with alterations, was issued in 1216 and 1225, it continued to be a subject of contention for many centuries as it was seen by later monarchs as restricting their authority as the Church in England would be free from the interference by the Crown.