Yes, minors accompanied by their parents/guardian is a whole different critter than a minor alone. If something were to happen; injury, sickness, or otherwise, the parent/guardian is there to tend to the child. If not, there is no one to authorize any care that may be needed. That is a law suit just waiting for the lawyer to be selected.

Given you need to be a member (whether paid or temporary) to gain access to the club the agent was correct. I also have no doubt this is such a corner case that no one at AA has given any thought to how to handle this. I would suggest writing to AA, explain your situation, and see if they have any suggestions. It may be possible to have one of the AAngels to "guest" you into the club.