Calvin:

The Role of the Father:

1) That, then, is the intention of our Lord Jesus. For He surely prayed throughout His whole life, and even previously in this great combat which He had sustained, He prays to God that if it were possible this drink might be turned away from Him. But now He has taken up His conclusion, because He was so ordained by God His Father and He saw that He must acquit Himself of the charge which was committed to Him, that is, to offer the perpetual sacrifice to blot out the sins of the world. John Calvin, Sermons on the Deity of Christ, Sermon 5, Matt 25:51-56 , p., 87.

2) Therefore Jesus Christ will not answer before Pontius Pilate. Why so? Because he sought to satisfy the will of God his father, & that decree which he had concluded: he knew that by his sacrifice, he puts away the sins of the world. And therefore Jesus Christ being in the place of sinners, & their persons, defended not himself: & as it has been said by the Prophet Isaiah, he is led to death, as a lamb that is shorn and opens not his mouth…

To be short this is that the Apostle says in the tenth of Hebrews, if we will be partakers of all that was gotten us by the son of God, we must have patience: after that he has shown himself, that when Jesus Christ had suffered for the sins of the world, he went up into heaven, he added “That this was to arm us to patience.” For it is nothing, if the fruit of this redemption, which was purchased for us, does not show itself by faith: for otherwise, it will be a thing come to nought. John Calvin, Sermons on 1 Timothy, Sermon 51, 6:13-16, p., 612.

The Office of the Spirit:

1) He calls the Spirit another Comforter, on account of the difference between the blessings which we obtain from both. The peculiar office of Christ was, to appease the wrath of God by atoning for the sins of the world, to redeem men from death, to procure righteousness and life; and the peculiar office of the Spirit is, to make us partakers not only of Christ himself, but of all his blessings. And yet there would be no impropriety in inferring from this passage a distinction of Persons; for there must be some peculiarity in which the Spirit differs from the Son so as to be another than the Son. John Calvin, John 14:16.

2) “Unto obedience”. He adds two things to sanctification, and seems to understand newness of life by obedience, and by the sprinkling of the blood of Christ the remission of sins. But if these be parts or effects of sanctification, then sanctification is to be taken here somewhat different from what it means when used by Paul, that is, more generally. God then sanctifies us by an effectual calling; and this is done when we are renewed to an obedience to his righteousness, and when we are sprinkled by the blood of Christ, and thus are cleansed from our sins. And there seems to be an implied allusion to the ancient rite of sprinkling used under the law. For as it was not then sufficient for the victim to be slain and the blood to be poured out, except the people were sprinkled; so now the blood of Christ which has been shed will avail us nothing, except our consciences are by it cleansed. There is then to be understood here a contrast, that, as formerly under the law the sprinkling of blood was made by the hand of the priest; so now the Holy Spirit sprinkles our souls with the blood of Christ for the expiation of our sins. John Calvin, 1 Peter 1:1-2.

[Note: these are but a few informal references from Calvin on the Trinitarian work of salvation which demonstrate the impropriety of positing a disconnect between the work of the Father and the work of the Son in the classic and moderate understanding of the extent and nature of the expiation.]