Since you are a voluntary geographical bachelor, you are not entitled to reside in military housing, barracks or bachelor housing. That is established in the Joint Federal Travel Regulation (JFTR). If the you desire to live in the barracks, you may have the option to voluntarily give up BAH, and live in the barracks. I know this puts a financial hit on your family income, but you can’t legal have both.
Think of it like this: A Soldier lives in family housing with his dependents (not drawing BAH). His dependents move out for whatever reason. Now, he wants to remain in housing, but start drawing BAH to support his dependents. It is not legal. Basically the same standard applies to your situation.