Attending AA voluntarily might certainly help as it may make the judge more sympathetic to your case. At the very least, and probably even more importantly, your continued attendance at AA may address the root cause of your driving while intoxicated, especially if it is a habitual thing. So it might just actually prevent you from coming back on here and having to ask a question like this again. And do get an attorney to represent you at your upcoming court date. Best of luck.
I have seen many excellent public defenders though most of them are overwhelmed by the workload that they are presented with. I would still look at hiring an experienced DUI attorney, as they can best elevate your chances of a more favorable outcome (or mitigating the damages of an unfavorable one). These are pretty serious charges and the stakes are high. You may find the investment to be worth it. Most will offer you a free consultation and many will offer installment payments. Best of luck.
Transferring the home to the kids may be a very good option. The look back period on Medicaid is 5 years, but this must be done carefully and preferably, with the guidance of an experienced elder care attorney. Many attorneys, myself included, offer a free consultation. It's important that you act sooner, rather than later, on this. Best of luck on the matter.