Hello and thank you for entrusting me to assist you. My name is ***** ***** I will do everything I can to answer your question.
I can't imagine any employer in their right mind wanting to continue employing someone like this. However, there is nothing illegal about employing someone with DUIs, or even someone who comes to work drunk. Obviously, this creates massive liability issues for the company, reduces the morale of the remaining employees, and is generally just "bad business," but it is their company and they can manage it however they see fit. You do not have a leave right to dictate who your employer can or cannot employ, or what discipline they should or should not take against given individuals.
Now, the above noted, your employer does appear to be operating on the misunderstanding that they cannot take adverse employment action against someone for drinking and drinking-related criminal offenses if that person is an alcoholic. This is not true. Alcoholism is a protected "disability," but all this really means is that an employer cannot take adverse action against someone merely because they are PERCEIVED as an alcoholic. But having alcoholism is not a "pass" to drink on the job--drinking on the job is punishable no matter what underlying disease may cause it. And if driving is any part of this employee's job duties, the past DUI convictions would certainly be a sufficient basis for termination as well. (If driving isn't part of the job, the convictions may still be proper grounds for dismissal, but the law is more complicated and less clear in this circumstance.)
You may wish to view what the EEOC has to say about alcoholism and disability laws here. Perhaps if you give this information to your employer, they will reconsider their position regarding this individual. But all you can do is attempt to persuade. You have no legal ground to force their hand here.
I hope that you find this information helpful. Please do not hesitate to let me know if you have any questions or concerns regarding the above and I will be more than happy to assist you further.
If you do not require any further assistance, please be so kind as to provide a positive rating of my service so that I may receive credit for assisting you. Very best wishes moving forward.