Do you have to move out of on-post housing following a divorce?

https://www.defensetravel.dod.mil/site/faqbah.cfm#:~:text=When%20the%20former%20spouses%20share,child%20during%20the%20same%20period.

I am divorced with children, what is my BAH allowance?

It depends on whether or not you have legal and physical custody of your children, pay child support, and/or live in single-type Gov't quarters. If you have legal and physical custody of your children, then you are authorized BAH at the with-dependent rate if not assigned adequate family-type Gov't quarters. If your former spouse has custody and you are paying adequate child support (at least in an amount of your BAH-DIFF rate) you are authorized BAH at the with-dependent rate if not in Gov't quarters or BAH-DIFF if assigned single-type Gov't quarters.

What is BAH-Diff?

BAH-DIFF is the housing allowance amount for a member who is assigned to single-type quarters and who is authorized a BAH solely by reason of the member's payment of child support. A member is not authorized BAH-DIFF if the monthly rate of that child support is less than the BAH-DIFF amount. The BAH-DIFF amounts, originally calculated in 1997, are updated annually based on changes in the Basic Pay tables. For more information contact your servicing finance office or consult DoDFMR, Volume 7A, pars. 260301 and 260504.

This is from Defense Travel Management Office website so seems to be DoD wide applies in this way.

If you don't have any dependents, yes you'd have to move out of on base housing since those are all "family" housing.

If you have any dependents, you should be able to say in housing.

Talk to your housing contact.

Unless you have primary custody of the child(ren), you are more than likely going to have to move out of base housing. However, I am answering with almost 20 years worth of old information. Contact your housing office for a definitive answer.