The reason no one jumped in to answer your questions is that there are so many variables, it is difficult to know what has happened or where to suggest you go for help. However, undersantding that this is not legal advice and that you need to consult a lawyer licensed in your jurisdiction, let me try to help send you in a useful direction.
First, it sounds like you are a family member of the defendant. So, the lawyer for the defendant has no duty -- and cannot without express consent of the defendant -- discuss confidential matters with you. This often leads to frustration and a lack of information on the part of family members.
Second, it seems that there has been some communication between the defendant and his lawyer since it appears that he has been in court and taken certain actions -- but, it is not clear.
Third, however, if there really is no communication between the defendant and his lawyer for four months and a critical court appearance is coming up, that does seem problematic. The public defender should know what has to be done and what communications are necessary in order to accomplish it. But we all know that there are situations where lawyers, whether public defenders or otherwise, have dropped the ball.
Fourth, you talk about some sort of transfer from one facility to another -- I have no idea what that is about. Is it due to overcrowding or does the defendnat have another case pending in another county? As indicated below, an experienced local attorney should be able to shed some light on this.
Fifth, there are remedies that a person can pursue if held in custody without being able to see his lawyer, including a Writ of Habeas Corpus. Except in extreme circumstances, that is not something that should be initiated, except by the person in custody. There may be much more to the dynamics of this case than you are aware.
Sixth, I would suggest that you find an experienced criminal defense lawyer in the area and make an appointment. Even if you cannot afford to hire a lawyer to take over the case, usually an experienced lawyer will take the time to talk with you and try to get to the bottom of the facts. She or he can give you much better information and some actual legal advice.
Best of luck.