2. "I offer You the Body and Blood, Soul and Divinity of Your dearly beloved Son, our Lord Jesus Christ"
Notice that what we here "offer" to the Father is what He sees from all eternity: the self-offering and self-sacrifice of His Son. We "offer" this to Him in the sense that we pray all our Chaplets to the Father solely on the basis of what is most precious to Him in the whole universe. Namely, the loving obedience unto death of Jesus His Son.
So, we "offer" Christ's sacrifice to the Father in the sense that all our pleas to the Father for an outpouring of His mercy upon the world are made solely on the basis of Christ's perfect sacrifice to the Father, with all its superabundant merits, and we pray that all the graces that Jesus merited for us by His life and death may be poured out upon us.
In this way, also, we join our Chaplet prayers on earth with the pleading of the heavenly Jesus Christ, who continues forever in heaven as our "advocate" and "intercessor":
If any one does sin, we have an advocate with the Father, Jesus Christ the righteous, and He is the expiation for our sins, and not for ours only, but for the sins of the whole world (1 Jn 2:1).
[Christ] hold His priesthood permanently because He continues forever. Consequently, He is able for all time to save those who draw near to God through Him, since He always lives to make intercession for them (Heb 7:25).
Most importantly, you will recognize that all this is precisely the same thing that happens at every Mass. Catechism 1374, quoting the 16th century ecumenical Council of Trent, states: "In the Most Blessed Sacrament of the Eucharist, the Body and Blood, together with the Soul and Divinity of our Lord Jesus Christ, and therefore the whole Christ, is truly, really, and substantially contained."
This is the answer to your particular question, John. Trent was responding to those Protestant critics at the time who misconstrued the Catholic doctrine of the Real Presence, as if it meant that we receive merely the material elements of Jesus' Body and Blood. Whereas Catholic belief is that those words are just "shorthand" for the fullness of the Eucharistic mystery: that we receive the living and glorified Body and Blood of our heavenly Advocate and Intercessor, Jesus Christ, in every Holy Communion. For a living body is a body united to its soul, and a glorified human being is a body and soul united with divinity. Therefore, in the Eucharist we receive and enjoy an intimate and deeply personal relationship with Jesus Christ in the fullness of all that He is, and we unite ourselves completely with His earthly sacrifice and heavenly pleading on our behalf.
The Council of Trent also taught that by offering Christ to the Father in the Eucharist (that is, by offering our prayers in union with His sacrifice and prayers to the Father) we make a truly "propitiatory" offering for our sins. In other words, an offering that covers and makes up for the debt to God's justice that we incurred by our sins. Similarly, in the Chaplet, we extend this same Eucharistic offering: We offer up the whole Christ, Body and Blood, Soul and Divinity, as the next line says ...
3. " ... in atonement for our sins, and those of the whole world."