You have a Sixth Amendment Right to Counsel. That is the right to have an attorney of your choosing if you want to hire them. You have a right to fire your attorney as well. However, in certain circumstances a judge may not agree to allow an attorney to withdraw. Has your attorney filed a substitution, have you stated on the record, or told your court appointed attorney that he/she is fired. By hiring an attorney it seems as though that there has been a break down in the attorney-client relationship. You may need to have your attorneys articulate these points on the record. Your court appointed attorney should file a Motion to Withdraw based on the above stated reasons.
I have seen this happen in Detroit. Court appointed was orderd to stay on as "co-counsel" because the judge did not want to delay the trial. New counsel needed time to get up tp speed and the judge did not want to give the additional time. If this is what is going on, the judge is-in my opinion-violating your right to counsel by not allowing your attorney of choice to take over. I assume that the appropriate objections have been made on the record. If not, a record should be made to preserve the issue for appeal.
I can think of many ways to challenge the judge's ruling, as the right to counsel of choice is a right more strongly protected by the higher courts than many rights. Your hired attorney should be making the appropriate motions and arguments, and supporting them with appropriate case law. If he is not doing that, then maybe he is not that good, and you might benefit from having the appointed attorney stick around. I have trouble believing that Wayne County is paying for an unneeded lawyer, given that they are real short of money right now, but whatever the judge orders, that is the way it will be, until and unless the case reaches the Court of Appeals.
Contact me at 248-399-6930 for a free consultation. You and I do not have an attorney-client relationship formed by our communications on this website. Advice given by me on this website is general advice based on partial information. You should not rely on any advice given without first hiring a lawyer in the area where the case is pending, and providing that lawyer with full information.