During the arraignment you are told of the charges against you and advised you have the right to an attorney. If this process is complete, the next step is generally a pre-preliminary hearing. At this hearing, discovery is exchanged and the district attorney will generally give an indicated offer in the case. The next court date is a generally a preliminary hearing. At this hearing the district attorney will have to put on evidence to convince the judge to bound you over for trial.
It looks as though your son was cited for a misdemeanor and released. The citation will list the charge that the your son was charged with violating. Generally, after an officer cites an individual the citation is forwarded to the District Attorney's office for review. If your case is not on calendar you can call the District Attorney's office if a complaint has been filed.
If you are charged with your first DUI the charges should be 23152a/23152b as a misdemeanor. An attorney can appear on your behalf and you will not need to be personally present. It is important that you attend the court date if you do not hire any attorney. Failing to attend a court date will lead to the judge issuing a bench warrant.
A public defender is a great attorney. However, you should be aware that there might be diversion programs available for first-time offenders. (Depending on the facts of your case) Secondly, a drunk in public might have negative consequences in your family law case. You do not want to give your former girlfriend ammunition to use in your current custody battle.
It is unlikely that the warrant was dropped. In some situations, warrants may not come up in the officer's system. I would suggest contacting a criminal defense attorney who can research if an active warrant still exists. An attorney may also have grounds to file a Serna motion on behalf of your boyfriend.
I also agree with the previous answers to your question posted by several of my colleagues. In some counties, the District Attorney's Office offers pre-plea diversion programs. The availability of these programs varies from county to county and an individual's previous record, age, and amount taken are all considered in gauging if he/she qualifies for the program.