That in the union, the two distinct wills act in perfect unity as one
Yet their unity is so perfect so as to be regarded as one will.
To emphasise the point further in both negative and positive terms: their unity constitutes one will, not because the unity obliterates the distinction, but because the unity is perfect, real, and hypostatic. This was the general justification given by St. Cyril with respect to his one nature formula in his letter to Bishop Succensus, and it applies here in respect to will and operation.
Would you care to define what you mean by the words "volition" and "faculty"?
"Volition" can better be contrasted with "volitional capacity." The former is the "decision", the latter is the "mode of willing." Confusion arises because the unqualified term "will" can be applied to both categories. The Catholic Encyclopedia has an interesting way of qualifying the term 'will' to distinguish its application according to the above two categories: the former is the, "will willed", and the latter is the "will willing." Thus, our confession of "one will" ("one decision", "one volition", one "will willed") safeguards the fact that the natural human will and natural divine will of Christ, are indeed hypostasised by one subject--the hypostasis of God the Word--such that they are necessarily unified by Him--a unity which is expressed by the one ultimate decision made.
How do you respond to this allegation?
I would respond to Bishop Auxentios by encouraging him to actually read what the Oriental Orthodox Fathers had to say on the matter, as opposed to continuing the tradition of false and unwarranted presumption and ignorance. The dual consubstantiality of Christ is one of the most explicit points made in the Christological works of the OO Fathers that one who has actually read them is quite hard-pressed to miss it.
The very exact phrases “consubstantial with the Father” and “consubstantial with us/mankind”, are explicitly confessed hand in hand in the individual works of Sts. Dioscoros of Alexandria, Timothy of Alexandria, Severus of Antioch, Philoxenus of Mabbug, confessed unanimously by the consensus of OO Hierarchs in the confession presented to Emperor Justinian (which seems quite likely to have influenced the very judgments made at Constantinople 553), and confirmed unequivocally in various Synods held both in Antioch and Alexandria. Anyone who did not confess similarly, was ex-communicated and under anathema.
If you would like exact quotations I can provide them; they’ll all be more or less the same, having in common the relevant phrases, “consubstantial with the Father” and “consubstantial with us”, word for word. How much more explicit can one be on “dual consubstantiality”?