The short answer is yes, one can be charged with DUI even though they are not arrested and did not have their rights read to them. The longer answer is that if your husband is facing a court-martial he needs to seek base legal counsel and consider retaining a civilian attorney.
Understand two things: One, if you are not comfortable with your lawyer, you should tell him so and you should consult with another lawyer.
Two, your lawyer is getting paid a portion of your recovery. There would be no incentive for him to "work for the other side" and get you (and him) less money.
I have dealt with several of these cases. You need to contact your unit ASAP, and see if they can arrange an alternate duty location for you. If not, regardless of the logistical problems you need to report. The long term negative implication of an Other Than Honorable Discharge (which is what you will get if you don't report) are significant and far outweigh any logistical issues. Make sure all your paperwork is in order. You might want to contact a military law attorney prior to...