You'd have to give me a specific example of a conflict between the three. But certainly there exist, at the very least, apparent contradictions that require clarification.
So, from a logical perspective, the Church is the ultimate Authority since, without the Church to write, preserve and canonize Scripture, or to preserve and recognize Apostolic Tradition, the other two pillars of Christian teaching authority would be thrown into doubt.
We also have the words of Jesus.
“If your brother or sister sins, go and point out their fault, just between the two of you. If they listen to you, you have won them over. But if they will not listen, take one or two others along, so that ‘every matter may be established by the testimony of two or three witnesses.’ If they still refuse to listen, tell it to the church; and if they refuse to listen even to the church, treat them as you would a pagan or a tax collector.Keep in mind that Jesus could have said, "take it to Me." But he said, take it "to the church." So the Church must teach with equal Authority to that of Christ, even though the Church does not possess the entire Mind of Christ. But when the Church teaches definitively, It teaches with the Authority of Christ.
Other logical conclusions follow. Jesus could not have been speaking of an invisible church, since it's impossible for an invisible church to arbitrate disputes.
This church must also possess a unified, non-contradictory body of doctrine. Otherwise, It could not settle doctrinal disputes, such as, what constitutes a sin or "fault."
"Then Joseph, being aroused from sleep, did as the angel of the Lord commanded him and took to him his wife, and did not know her till (emphasis added) she had brought forth her firstborn Son.fn And he called His name JESUS." Matthew 1:24-25
Also, the RCC Catechism teaches:
(1601) The matrimonial covenant, by which a man and a woman establish between themselves a partnership of the whole of life, is by its nature ordered toward the good of the spouses and the procreation and education of offspring; this covenant between baptized persons has been raised by Christ the Lord to the dignity of a sacrament.
(1620) Both the sacrament of Matrimony and virginity for the Kingdom of God come from the Lord himself. It is he who gives them meaning and grants them the grace which is indispensable for living them out in conformity with his will. Esteem of virginity for the sake of the kingdom and the Christian understanding of marriage are inseparable, and they reinforce each other:
Whoever denigrates marriage also diminishes the glory of virginity. Whoever praises it makes virginity more admirable and resplendent. What appears good only in comparison with evil would not be truly good. The most excellent good is something even better than what is admitted to be good.
(1640) Thus the marriage bond has been established by God himself in such a way that a marriage concluded and consummated between baptized persons can never be dissolved. This bond, which results from the free human act of the spouses and their consummation of the marriage, is a reality, henceforth irrevocable, and gives rise to a covenant guaranteed by God's fidelity. The Church does not have the power to contravene this disposition of divine wisdom.
(2335) Each of the two sexes is an image of the power and tenderness of God, with equal dignity though in a different way. The union of man and woman in marriage is a way of imitating in the flesh the Creator's generosity and fecundity: "Therefore a man leaves his father and his mother and cleaves to his wife, and they become one flesh." All human generations proceed from this union.
So, was Mary married to Joseph as the Scriptures and the RCC teach, or is she a perpetual virgin as the RCC teaches?