If my wife doesn't want to PCS with me, will I still get BAH to pay for our family's housing while also being able to live in the barracks?

My apologies I am not PCSing more so she doesnt want to move away from her family once i get out of basic. So she doesnt want to move to my duty station

SGT (Join to see) - Sorry to hear that and unless she changes, at some point you may have to choose, Army or wife.

SGT (Join to see) - The Army did away with Geographical bachelors program years ago. An SM who is married can not under regulations stay in military barracks but with few exceptions.
If the military forces you in to an unaccompanied tour
On a very temp basis due to safety, security, investigative needs, or other emergency.
At your duty station, your 1SG MAY have control and access to unassigned rooms he can allow you to stay in......but it should be viewed as just a possibility, and temporary at that.
You are responsible in trade for receiving BAH to provide suitable housing for you and your spouse.. If you choose to live in seperate locations that is on you to provide for as well.

SGT (Join to see) - sorry to be blunt but this is something you should have ironed out before you got married or before you enlisted. Since you are married, the Army will either provide on post housing (depending on availability) or pay you BAH. Married soldiers are not allowed to live in the barracks. So you will have to choose between paying for a place for you to live or paying for a place for your wife and kids to live. AS far as I know, the only exceptions are when you are assigned a duty station where your dependents cannot accompany you. "my wife doesn't want to leave her family" isn't going to qualify you as a geographical bachelor.