It follows from our understanding of punishment that the proper reason for punishment should be invoked by the sentencing judge in sequence.
If it is possible to punish the criminal with the same harm and of the same kind he inflicted upon the victim, then this is what should be done. This will incidentally serve to rehabilitate.
If that’s not possible, then at least deal the same amount of harm even in some generic non-cruel-or-unusual manner, such as a fine or prison term. This is retribution.
If even this cannot be done, the judge should at least try to maximize social welfare (while considering the criminal to be a member of society) by calibrating the harm to the criminal to be smaller than the social benefit of the reinforcement of deterrence.
And if that does not work either, then the criminal should be cut off from society as a cancerous cell from the body and imprisoned for life or executed.
We can see from this that retribution is prior to deterrence, so Rothbard is right in favoring the former over the latter. But he is mistaken in criticizing rehabilitation as some sort of psychological brainwashing in an insane asylum; rehabilitation is simply a refined version of retribution designed to make the offender feel exactly as bad as he made his victim feel.