Consequently, although the Son had a free choice in the matter of His death, it was a fixed choice.... Thus, Christ freely chose what was fixed from God.I regret that I cannot find the Latin original so I could see what word is translated as "fixed." My educated guess is that Anselm used the past participle of the verb figere (to fasten). (Cf. the past passive participle of the compound verb crucifixus, meaning to be fastened on a cross.)
Latin participles are non-finite (i.e. they are not inflected as to subject) verbal adjectives; consequently, assuming the past participle of figere, there is no subject to whom we can attribute Christ's "fixed choice." So, as I understand Anselm, Christ's "fixed choice" was a resolute human choice (or if you prefer, a decision) to suffer death, as opposed to a predetermined divine choice.
Anselm clearly states that God drew and move Christ's human will since God the Father gave Christ that will.