What can I do if I am a green card holder arrested for domestic violence?

Unfortunately this is a very complicated question. As far as your paperwork, there is a chance that it was already processed. On the other hand, this could delay things quite a bit. Ultimately, a lot will depend on the charges against you, and the final disposition of your criminal case. I would strongly advise you to retain a criminal lawyer familiar with the immigration consequences of criminal convictions (or a criminal attorney and an immigration attorney) as some convictions can lead to deportation, even for a green card holder. It could also impact your ability/timing to obtain citizenship down the road.

Your question requires an attorney consultation. It is not a simple question that can be answered on this type of forum. There are many factors that would need to be considered and evaluated. Although you have not been convicted, you have been arrested. If you are scheduled for an interview, and are asked about any arrest, you will have to admit to the arrest and probably have to explain to the immigration officer the facts surrounding the arrest. The fact that your wife wants to drop charges, may or may not help you. Once a police report has been made, the allegations and charges are sent to the District Attorney to determine whether to file charges with the court. The decision to file charges, reduce charges, prosecute a case or dismiss a case is solely at the discretion of the District Attorney or Prosecuting Attorney. Although the "victim" (your wife) may wish to have the charges dropped or dismissed, the final decision will be up to the D.A. Domestic violence is characterized as a crime of violence which will make you deportable, if convicted. I strongly suggest that you contact an experienced immigration and criminal defense attorney for a face-to-face consultation and give them all of the facts surrounding your situation. They would then be in a better position to analyze your case and advise you of your options.