Do I have to prove detailed arrest information to an employer?

As a DUI attorney I can't answer this specifically, I notice this was also posted on an employment law forum, they will have the better legal answer. The nature of your job, job requirements and whether you have a contract will determine whether or not you have to provide the requested information. If you are an "at-will" employee I think you don't have to provide the information, however your employer may choose to terminate you too.

It is CONVICIONS not arrests that they are asking about. the answer is yes since if you drive a vehicle for them, then it affects their liability.

You used the term "deputy director" which leads me to believe you may work for a government. If so, this answer COULD BE different. Generally, any private employer may ask you for anything, and you may be discharged for failing to do so. If so, you likely would have no remedy against the employer. Georgia recognizes the doctrine of employment at will. Employment at will means that in the absence of a written contract of employment for a defined duration, an employer can terminate an employee for good cause, bad cause, a mistaken cause, or no cause at all, so long as it is not an illegal cause.

If your job duties include the need to have a valid driver's license or your alcohol use/abuse that cause your DUI could be found to be "substantially related" to your job duties, then it could be reasonable for your employer to request some information and documents regarding your arrest and conviction. You should contact an attorney and provide everything to the attorney for an adequate evaluation of your situation.

Generally, no one is required to provide anything, however, in an at-will employment relationship, you could be fired for failure to provide requested documents. At the same time, if you get fired, you could have a legal claim.

Yes, you are legally required to provide it. In any employment situation, the employer has control of the employee on matters that are related to work. I do not know the reasons or the motive for the employer asking for the details of your arrest and conviction records, but I presume that they are related to your work somehow. The employer has an interest in having a sane, sober and sound employee who is productive. If you fail to provide them, the employer can take disciplinary action against you. You cannot assert the right of privacy or 5th amendment privilege either because you have been convicted and those records are a matter of publc records now. Good luck.