Dear Moshe,
I miss you and understand your dilemma, though we have not spoken in some time. Most of what I write below I believe is in line with Alcoholics Anonymous, chapters 8 and 9. After you read them and put them into action, things will be different. Do not suggest your wife read them - this is for you. I strongly suggest you read them soon.
Based on what you wrote, two things are clear to me and my suggestions will be as obvious:
1- Yes, your recovery comes first, and yes, you are scared and have every right to be. But you have gone to meetings that were at times that were very inconvenient for your wife. That was a mistake.
Doing that is saying to your wife, "To hell with you - I'm taking care of myself", and that is silly. There is no compromise when it comes to honesty and recovery - but when it comes to human relations and marriage, there is nothing BUT compromise.
There must be meetings available at times that are easier for your wife and kids. And even if the meetings you must go to ARE at bad times for them, you should be able to do something extra for your wife in return for the time you go off to meetings. Your recovery is worth that. Work with the woman!!
OK. Now as far as divorce, I believe that as usual (sorry) you are making a bigger deal out of this that it really is. I even spoke with my own wife about this issue today (she does not know you, nor does she care who you are) and she admitted to me that all the times she said she'd divorce me if x, y, or z, were all lies. Lies to herself.
Your wife is hurting badly, She is bleeding from her heart. She does not understand all this recovery mumbo jumbo and it seems to her like another one of your extremist, excited, and self-centered plans - this one impacting her terribly.
She can't take it.
But she will NOT divorce you over it, if you truly get into recovery, for you WILL become a better person to live with. She will know this.
Why does she know anything you share that is about your personal life there, anyway? What does she mean by this? Have you told her that you share about when she goes to the mikvah, or how she likes or doesn't like to have sex with you, in the meetings? And if you did, have you told her about that? Why? Did you make the common mistake of bringing our wives into our inner nuttiness? That is far more a proof of dependence than the fear of going to meetings - for the reason we typically tell our wives all the details they do not need to hear, is cuz we are so desperate for their approval and sympathy. More childish self-centeredness. If that's what you are doing, then quit it, man. Respect her enough not to vomit on her again.
And if that is not it, and instead she is just upset and scared because she does not trust anonymity and thinks you will be outed in your community and she will lose her reputation over your behavior coming out - then she is just plain wrong. But you can STILL work with her on that! Explain the way meetings work to her - that it is only sexaholics, not the public, and maybe even make an agreement with her that you will only open up partially in the meetings, and only FULLY with your sponsor. Just an idea. Nu, I do not know - but SOME compromise can be made with her. It will probably only need to be kept for a few months - as you start to get better, she will see it first (before you do) and then you can discuss with her that you want to open up fully even in the meetings.
I am sorry if your CODA or SLA sponsor feels that you must get free of her at all costs first no matter what, so that you recover from your dependence on her, too. But even doing THAT can be done like a mentch. She married a mentch...didn't she? Where is room for love? That needs to be asked. Practicing freedom from dependency must be done by expressing TRUE love. Not just more self-centered extremism. That's not recovery, and will not lead to recovery for anybody.
Gevalt. Do recovery fully, give yourself totally to this program of recovery and to your G-d with complete abandon - but don't do it like a baby. You are married man. Start acting like one, Moshe. Be as kind as you can while you get the job done.
I admire and love you very much (but a lot less and a lot differently than your wife does, I am sure),
Dov