What I get from that is that she hasn't accepted or believes she has a problem even thought she is going to AA. Or am I wrong?
I think that assumption would be reaching a bit. She may just be embarrassed. There is a lot of stigma surrounding alcohol abuse and also programs like AA.
But I do think you have a right to share what your experiencing with family and friends as you see fit.
I shared with my close family and friends who I knew I could look to for my own support, or to support my family (myself and my husband)
Curious, how word got back to your wife. Did you tell her, did the news spread in a gossip sort of way, or did that person contact her to offer support? Maybe the context of how she found out others knew' contributed to her feelings?