What channels can lawyers who are refused criminal detention complain to?

You didn't make it clear. Is it administrative detention or criminal detention? In the case of administrative detention, because it is an administrative act, you can apply for reconsideration to the higher authorities that made the decision according to the Administrative Reconsideration Law, bring a lawsuit to the people's court according to the Administrative Procedure Law, or conduct letters and visits according to the Regulations on Letters and Visits. In the case of criminal detention, you can appeal to the court or the procuratorate, because according to the provisions of the Criminal Procedure Law, if the people's court or the people's procuratorate finds that the compulsory measures taken against the criminal suspect or defendant are improper, it should be revoked or changed in time. When the people's procuratorate examines and approves the arrest, it finds that the investigation activities of the public security organ are illegal, and it shall notify the public security organ to make corrections, and the public security organ shall notify the people's procuratorate of the corrections. Of course, in either case, you can complain to the organ that made the decision, to the people's congress with extensive supervision power, or to the disciplinary Committee of our party about the violation of discipline and law by the relevant personnel. Those who violate the law will of course be subject to disciplinary sanctions within the party and administrative sanctions within the organs, and those who seriously neglect their duties will be investigated by criminal law.