Well, well.. After reading several responses, I sure can say that I have read some things that seem helpful and some things that seem like people just going out of their way to be ugly which is not helpful at all.
I am also a Catholic and share a similar feeling about this group. It goes against what the church believes and I would not want any children of mine ever knowing about my family being involved in it if they were. That being said, your husband is part of the group already so what do you do now?
You have clearly expressed to him that you don't want him to be involved and he honestly doesn't really seem to care. I'm not sure if he converted to Catholicism or not, or you were married in the Catholic church, but him picking some club thing because of his late mother something or other just seems like an excuse for him to do something he has clearly thought about doing for a long time now. You are also bonded with him spiritually, so frankly you should be coming first in his life, not his mother or some boys club. At this point I would talk to your pastor about it. They always have wonderful advice for me when I am struggling with anything, and honestly.. I'm sure several of them have heard of this EXACT same problem before. I would not get involved with the group at all and wouldn't let your kids know about it. Unfortunately, this decision does not just affect him.
Lastly, while I'm sure they are not A) a harmless organization who fantasizes about unicorns and rainbows while simultaneously holding fundraising events for Make-A-Wish, or B) a murderous bloodthirsty freaky ritual world-threatening group of people who worship satan and have druggy/shaman like rituatls, who really knows what goes on. All I'm saying is take everything you read with a grain of salt and know that the hanging from a neck whatever business you spoke of may just be some crazy stuff someone who knew nothing about it wrote.
Just try to remain calm and seek help. You obviously need to talk to someone about this and while some people on the forum may have family members involved, that doesn't mean they are going to be helpful. Seek advice from your parish and pray. Good luck sorting this out and don't let anyone talk you down from being concerned or freak you out and make you go nutso.