A private club has the right to set its own policies... as to who it will and will not allow in or recognize or extend benefits to. This isn't a public accomadation, but a private club. Frankly I think they should just not extend this particular person an invite back after her current membership expires and be done with it.
As someone very involved in the operation of a private club (as a member), I can tell you that the government can wield a lot of pressure...threatening the cancellation of liquor licenses, threatening the cancellation of leases, enforcing anti-smoking restrictions by legislative fiat, threatening extra scrutiny on construction permit applications, workers' comp claims, etc. It's very intimidating. Of course, all of this happened to us under a RAT adminstration.
Better yet, refund her dues and cancel her current membership.