You should not be paying taxes if you are only in Maryland for her military service. You are protected by the Military Spouse Residency Relief Act  (MSRRA) which means you do not need to pay state income taxes in any state where you are not a legal resident and are in only for the military.

You need to file a Maryland Non-resident tax return to get the money back and you need to notify your employer that you are protected under MSRRA and request that they stop taking Maryland taxes out.

Each state has a different form from their own Department of Revenue, so look online to find which form Maryland requires, fill it out and give to your employer with a copy of your military orders.