Assuming this case is a misdemenor, in some states three or more DUI's can result in a felony complaint being issued. But the important thing is to have an attorney present in court so a warrant for his arrest will not be issued for Failure to Appear in addition to DUI charge.  If  you can afford an attorney hire one, who can at least make a "special appearance" and get the hearing postponed. If it's a misdemenor the attorney can appear without your brother being present in most cases, even if he is ordered to be there by the court. Or, if you don't have the money, call the public defender for that courthouse for their advise. The important thing is do not ignore this.  In fact, it might be a good idea for your brother to call the court on the day of the hearing and if he is on his own, to explain the situation to the court and ask that any warrant that may issue, be held until he can return to answer the false charges against him. This also demonstrates personal responsibility.

But the important thing is to let the court know that he is out of state and cannot make his appearance on Monday.  I would not turn myself in to the authorities out of state, but if there is a warrant issued for failure to appear, you can go to court and ask that the warrant be recalled.

Since this is his third offense, I suggest he enroll in the various alcohol education programs such as Alcoholics Anonymous or if he has major medical insurance, to get into a rehabilityion program.  Make certain, however, that his participation is noted by the provider as proof that he is attending.