You can certainly attempt to sue your attorney. Additionally, you could start by contacting your state bar, they regulate the conduct of attorneys.
File a complaint with the Georgia Bar. See link below. They should help you get a refund.
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Lawyers have a set protocol on where they appear first when they have cases set at the same time which is a Superior Court rule. Felony cases come before misdemeanors. You should contact your lawyers office to see if they still represent you in your DUI case. Just because your lawyer cannot appear on Monday does not mean you will not have a lawyer on a later date. It is important that you speak with your lawyer to figure out what you need to do next to resolve your DUI case.