On the Catholic view of the atonement?

When I medidate on the Passion of Christ, I end up falling into the same doubts about the atonement, which I want to ask. The Catholic Church denies the penal substitutionary atonement, i.e. the notion Jesus presented himself before the Father so that He may be punished in our behalf. Instead, to atone for an offense is to offer to the offended something that he love equally or even more than he hated the offense, and so, because sin is an offense to God, the Church teaches that the sacrifice of Christ to the Father is this offering on our behalf, which, in virtue of Christ being the Son of God, is more pleasing to the Father than the whole collective of sin of human kind. Furthermore, the suffering, crucifixion and death of our Lord were meritorious of all grace to us, this making sense of the seven sacraments, the sacramentals and the spiritual authority of binding and losing of the Church. **My question:** I admit that my doubts, and thus my question, is half driven by emotions. My doubt is this: "Sacrifice" in more general therms can just mean offering for the sake of the one to whom we offer, e.g. I can offer to God my time in prayer and meditation, or my intellect in faith, or my will in obedience, for the sake that He is God, is the ultimate object of my desire. Then why did it needed for Christ sacrifice be in the sense of given His life to suffer and die on the cross, and not just an offering of Himself in this less bloodsheded way? I know that God could save us in any other way for Her is omnipotent, and that He choosed the cross because He thought of it as the fittest way. However, on this I reach another face of my doubt, i.e. when Christ was on the Getsemani He said: > Father, if it is possible, let this cup pass from me, but not as I will but as You will. Implying that His death on the cross was of the will of the Father. So, how then the Father pleases in the sacrifice of His Son that He wills? For, when I imagine my son sacrificing for the sake of another, I truly understand and can't help but to love my son for it, but not as my son sacrificing himself for the sake of my will. Again, this is half driven feelings, but these often get in the way of my spiritual life so I thought of getting rid of these. I appreciate any comment, and God bless.