The CEO is refusing to close the account and wants to ban her from visiting any branch location, while keeping the account open.
I don't know your culture, but I would advise that if you can't convince the CEO that closing this account is the only correct course of action, consider closing the account anyway, even if you're doing so in defiance of the CEO's wishes.
If you want to give one more shot at helping your CEO see the light first, your HR Officer could make a good ally. The branch staff could quite rightly complain that they have reported a hostile work environment and management has not taken steps to address it. (Barring the member from your premises is a necessary step. But doing so while holding on to her money could create a UDAAP issue.)
Assuming that you are the Board appointed Security Officer, also be sure to give this incident (and your resolution) an appropriate mention in your annual report.