If my mother is my dependent do I get BAH at her zip code or my duty station zip code?

The implied part of secondary dependents (DFAS term for your Mom, provided she is in DEERS as your dependent) is that they are so bad off they live WITH YOU. The second you draw BAH, you are ineligible for a barracks space. BAH is always the duty station, with the one exception being unaccompanied to Korea, then youd have to pick where she will go, and that is the BAH. Location enumerated in orders.

The mortgage, a rental, different locations, refusal to move, all irrelevant. Those are issues for you and your Mom to work out. You requested to add your Mom as a dependent. DFAS granted your request. You are on the hook to provide that support. This is the Faustian Bargain

RallyPoint requires our members to use their real names. Aliases, initials, joint names, email addresses, business promotions and fake names are not allowed. We know nicknames/callsigns are an important part of military culture and they may be annotated in quotations in conjunction with a first name. Profiles with fake names may be suspended and/or unverified unless changed.

https://rallypoint.force.com/Support/s/article/how-do-i-change-my-name-2020-03-13-10-21-35

BAH is always at the Soldiers location unless a very high level ETP comes down. If it wasn't, everyone would claim CT, Fairfax Cty, San Diego, and HI as their places of residence and get absurd amounts of BAH.