I was horrified at my first Alanon meeting, to come face to face with my Parish Priest. I had visions of him giving me a hard time in Confession for starters, and could not be comfortable thru that meeting.
He, bless him, came over and introduced himself with his Christian name, and whispered for me to not worry about him being there, just believe I needed to be there and so did he.
I heard him tell of his past as an A and son of A parents, and these stories were not what 99% of parishioners or fellow priests had known anything about.
I never breathed a word about Alanon or him, and no-one heard about me.
I reckon your mum is a bit shirty at not being in on your Alanon act, and has used the other member to get to you. I doubt anything has been divulged at all, and that mummy is playing her games.
Do as has been suggested, and let this other lass know that you do not speak about Alanon to anyone, least of all your mum....because she has no problem gossiping about anything.