How can people say "Father" to God if they have been tormented or abandoned by their earthly father/their earthly parents?
Human fathers and mothers often distort the image of a kind, fatherly God. Our Father in heaven, however, is not the same as our experiences of human parents. We must purify our image of God from all our own ideas so as to be able to encounter him with unconditional trust. Even individuals who have been raped by their own father can learn to pray the Our Father. Often it is their task in life to allow themselves to experience a love that was cruelly refused them by others but that nevertheless exists in a marvelous way, beyond all human imagining.
How are we changed by the Our Father?
The Our Father allows us to discover joyfully that we are children of one Father. Our common vocation is to praise our Father and to live together as though "of one heart and soul" (Acts 4:32). Because God the Father loves each of his children with the same exclusive love, as though we were the only object of his devotion, we too must get along together in a completely new way: peacefully, full of consideration and love, so that each one can be the awe-inspiring miracle that he actually is in God's sight.
(YOUCAT questions 516-517)
Dig Deeper: CCC section (2787-2791) and other references here.
Part 4: Christian Prayer (2558 - 2865)
Section 2: The Lord's Prayer (2759 - 2865)
Chapter 2: "Our Father Who art in Heaven" (2777 - 2802)
III. "OUR" FATHER ⇡
When we say "our" Father, we recognize first that all his promises of love announced by the prophets are fulfilled in the new and eternal covenant in his Christ: we have become "his" people and he is henceforth "our" God. This new relationship is the purely gratuitous gift of belonging to each other: we are to respond to "grace and truth" given us in Jesus Christ with love and faithfulness.45
45.
Jn 1:17; cf. Hos 2:21-22; 6:1-6.
Since the Lord's Prayer is that of his people in the "end-time," this "our" also expresses the certitude of our hope in God's ultimate promise: in the new Jerusalem he will say to the victor, "I will be his God and he shall be my son."46
46.
When we pray to "our" Father, we personally address the Father of our Lord Jesus Christ. By doing so we do not divide the Godhead, since the Father is its "source and origin," but rather confess that the Son is eternally begotten by him and the Holy Spirit proceeds from him. We are not confusing the persons, for we confess that our communion is with the Father and his Son, Jesus Christ, in their one Holy Spirit. The Holy Trinity is consubstantial and indivisible. When we pray to the Father, we adore and glorify him together with the Son and the Holy Spirit.
Grammatically, "our" qualifies a reality common to more than one person. There is only one God, and he is recognized as Father by those who, through faith in his only Son, are reborn of him by water and the Spirit.47 The Church is this new communion of God and men. United with the only Son, who has become "the firstborn among many brethren," she is in communion with one and the same Father in one and the same Holy Spirit.48 In praying "our" Father, each of the baptized is praying in this communion: "The company of those who believed were of one heart and soul."49
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For this reason, in spite of the divisions among Christians, this prayer to "our" Father remains our common patrimony and an urgent summons for all the baptized. In communion by faith in Christ and by Baptism, they ought to join in Jesus' prayer for the unity of his disciples.50
50.
Cf. UR 8; 22.