Yes, I would agree with part of your post. I believe that Anselm, correctly, believed the Father's and the Son's will were unique but consistent. In order for the wills to have been consistent, both wills would have to want the Son to die to the exact same degree, although how that would be expressed by the Father and the Son would be different. Moreover, and most importantly, Anselm makes the case that the Father gave the Son His human will with this purpose in mind so that it would remain steadfast to accomplishing the divine will. As Anselm states:
Our "free will" is like that, too. While it feels like we're acting according to our own reasoning and efforts, we are actually and completely carrying out God's plan for His creation, all ordained by God down to the very hairs on our head.
And because Jesus Christ is God, He knows this full well. Isaiah 53 tells us exactly what God's intentions are in Christ's birth, death and resurrection...
He is despised and rejected of men; a man of sorrows, and acquainted with grief: and we hid as it were our faces from him; he was despised, and we esteemed him not. Surely he hath borne our griefs, and carried our sorrows: yet we did esteem him stricken, smitten of God, and afflicted. But he was wounded for our transgressions, he was bruised for our iniquities: the chastisement of our peace was upon him; and with his stripes we are healed. All we like sheep have gone astray; we have turned every one to his own way; and the LORD hath laid on him the iniquity of us all. He was oppressed, and he was afflicted, yet he opened not his mouth: he is brought as a lamb to the slaughter, and as a sheep before her shearers is dumb, so he openeth not his mouth. He was taken from prison and from judgment: and who shall declare his generation? for he was cut off out of the land of the living: for the transgression of my people was he stricken. And he made his grave with the wicked, and with the rich in his death; because he had done no violence, neither was any deceit in his mouth. Yet it pleased the LORD to bruise him; he hath put him to grief: when thou shalt make his soul an offering for sin, he shall see his seed, he shall prolong his days, and the pleasure of the LORD shall prosper in his hand. He shall see of the travail of his soul, and shall be satisfied: by his knowledge shall my righteous servant justify many; for he shall bear their iniquities. Therefore will I divide him a portion with the great, and he shall divide the spoil with the strong; because he hath poured out his soul unto death: and he was numbered with the transgressors; and he bare the sin of many, and made intercession for the transgressors." -- Isaiah 53:2-12"For he shall grow up before him as a tender plant, and as a root out of a dry ground: he hath no form nor comeliness; and when we shall see him, there is no beauty that we should desire him.
Christ had to doubt and suffer and agonize because He was doing everything we should have done due to our many sins. God's perfect justice requires perfect recompense and as God tells us, we are incapable of giving it to Him. Only God Himself is equal to the task of wiping us clean by the blood of His Son. Christ became man to show man just how short he falls and just how far God will go to redeem His flock.
"He shall see of the travail of his soul, and shall be satisfied: by his knowledge shall my righteous servant justify many; for he shall bear their iniquities" -- Isaiah 53:11
Breathtaking, isn't it?
Anselm would disagree, as he expressly says "God did not, therefore, compel Christ to die; but he suffered death of his own will"; and then he proceeds to explain how "wish to die" means two different things with respect to the Father (who "desired the death of the Son, because he was not willing that the world should be saved in any other way") and the son (who "so earnestly desired the salvation of man, as if the Father had commanded him to die"). The Father's wish for Jesus to die is permissive and not compelling, and Jesus's human will is active and compels Him to undertake steps He knows will lead to the Cross.