You say you have contacted many organisations. Were none of them able to assist you with this issue?
One option you have is to submit a complaint about inaction on the part of the person in charge of your file. This is called ‘Untätigkeitsklage’ in German and can be submitted if there has been no action taken on an administrative matter (e.g. an application for family reunification) within three months. However, if your file has been sent recently to another city, then it is not a case of inaction. Is there really no connection between you and this other city?
Another option is to submit a formal complaint against the employee. This is called a ‘Dienstaufsichtsbeschwerde’ and can be made against an employee of an administrative authority. The employee’s actions would then have to be investigated. If you choose this option, however, it is important to have concrete proof for the complaint you are making. An accusation of lying is a serious matter and so you would have to have clear evidence in writing or have witnesses that this person lied and intentionally hindered your application.
Before exploring these options, it may be worth your while sending an inquiry in writing to the person in charge of your case. I would outline the situation in detail, the delay, the transfer of the file to another city, the impact it has on your family etc. I would set a deadline for a response and mention the possibility of taking further action if not answered within the deadline. Have you been communicating in writing with the person? It is best to have things in writing if possible.
You do not need a lawyer for such actions but some legal advice would be sensible. There are office called Refugee Law Clinics throughout Germany which offer free legal advice:
Otherwise, a local migration advisory service should be able to help you with this and also advocate on your behalf with the employee directly.