I would say that Christ not only knew the Fathers will but it was His will as well. The wills are the same.According to the one divine will, only the Son became man, so only the Son has a human will. Anselm seems to be exploring Christ's obedient submission of his human will to the one divine will.
I thought about that and I think you have a point in some of the writings above. Anselm states the following:
In this way, also, by following the will received from the Father invariably, and of his own accord, the Son became obedient to Him, even unto death; and learned obedience from the things which he suffered; that is, be learned how great was the work to be accomplished by obedience.
Since, therefore, the will of the Son pleased the Father, and be did not prevent him from choosing, or from fulfilling his choice, it is proper to say that he wished the Son to endure death so piously and for so great an object, though he was not pleased with his suffering. Moreover, he said that the cup must not pass from him, except he drank it, not because he could not have escaped death had he chosen to; but because, as has been said, the world could not otherwise be saved; and it was his fixed choice to stiffer death, rather than that the world should not be saved. It was for this reason, also, that he used those words, viz., to teach the human race that there was no other salvation for them but by his death; and not to show that he had no power at all to avoid death. For whatsoever things are said of him, similar to these which have been mentioned, they are all to be explained in accordance with the belief that he died, not by compulsion, but of free choice.