Arrested for DWI and appointed counsel deals with family law. How bad is that for my case?

In my earlier days, I did a lot of family law and now practice mostly in DWI defense, so I can relate to your question. The good news is that family lawyers spend a lot of time in CONTESTED court hearings so your lawyer will be less reluctance and have more ability to argue your case in court. Unfortunately, he will not be able to evaluate the video and other evidence and is unlikely to be knowledgeable of the 4th Amendment and other DWI issues. Perhaps, you will encourage him to consult with a DWI lawyer who can coach him on some of these issues before he advises you. But the fact is that you describe a physical & mental condition that makes it difficult for any lawyer to assess your situation. If you were so drunk that you passed out, as you described, then your case needs a plea bargain quickly. However, if other mental or physical conditions are the cause, you present a challenging situation for any lawyer. Drug reactions and other phenomena occasionally create situations such as yours and offer real challenges in the defense of DWI cases. You need to do a full written statement for your lawyer that describes exactly how you came to be in the place and condition that occurred when you were arrested. If you were intoxicated by either alcohol, drugs or both, you are likely to be pleading guilty and quickly, but if there are other possibe causes, you need to identify the source of your difficulty, consider a medical consult, prepare a detailed summary of your time line, consumption of alcohol or other substances and provide them to your attorney with a request that he discuss your situation with an experienced drug or DWI attorney

I don't practice in TX, but it's not good. DUI involves technical arguments based on specific law and facts. You need someone who knows what they are doing. Ask your lawyer about his experience.

Edward J. Blum