This is why it is important to have the right attorney from the beginning! Most attorney's would not get involved in the middle of a trial. Most attorney's will not take a case from another attorney in thier area.
If you really want a new lawyer, you would have to tell the Judge you wish to fire your attorney and wish to hire another. The Judge would then have the discretion. You would have to explain that your intention is not to cause delay, but that you are truely unhappy with the attorney. The judge could grant or deny your request. Make sure you put it on the record before the trial continues.
The trial itself would not just start over. The replacement attorney would have to start where the first attornet left off. Therefore, it is advised that you have your second attorney order a trial transcript so he knows what was said or done. In the very rare case, he might find something that could be grounds for a new trial or mistrial (which would give you a new trial).
You need to advise the judge that you wish to change attorneys at this time. You should have your new attorney hired and come to court with a prepared substitution of attorney form. The judge may deny your request or insist that the new attorney pick up where the old attorney left off. This is a time sensitive issue and should be addressed immediately if possible.
The Judge would likely not allow a substitution, because of delay, if you mean actually in the middle of a trial. Also this would not likely be in your best interest since the new attorney would not know what happened in the first part of the trial even if he could get the transcripts. The trial would not start anew for a voluntary substitution. If you mean in the middle of the case, not the trial, Judge Cassidy would likely allow this even if it meant a short delay, but not on the trial date, then it would be too late to substitute unless your new attorney agreed to no delay. As long as there is no delay especially on a dwi the Court usually will allow the substitution.