Hugs to you, djjdrjm. Betrayal at a time that should be the most bonding and special and yes, sacred, is shattering. I’m so sorry that he’s betrayed you so badly.
Others will be along quickly to offer a lot of great advice. The first thing is usually to make sure that you are focusing on and taking care of yourself and your kids first. You can’t be a good mom for them if you are not eating and hydrating and taking care of yourself, so please make sure that you focus on you and not on him. Don’t give in to the idea of helping him fix this if you’re having that urge. Only he can figure his shit out, and if he isn’t getting right on that in a very active (rather than just verbal) way, that should tell you something.
I just popped in to give you a hug of solidarity, and to say that true sex addiction isn’t nearly as common as cheaters who cry addiction when caught. Either way, this is HIS issue, not a couple issue. You will probably get many comments here saying that it is WAY too early for couples counseling. The marriage doesn’t have this problem (addiction?). HE DOES. The marriage didn’t cheat. HE DID. He needs to figure some things out before the two of you start working on the marriage.
You mention that he is in counseling already, but not every counselor is qualified to diagnose/treat port and sex addiction. If he hasn’t already gotten on finding a specialist and getting evaluated for that after saying that he has a porn/sex addiction, why do you think that is? If he really feels that he has a clinical disorder, he should want to immediately start getting treatment specifically for that—likely in addition to other counseling—so that he won’t continue to harm his wife and children? If it really isn’t just an excuse, what is he doing about it? Because you’re right: there’s the infidelity and then there’s the potential addictive behavior. They have to be addressed separately in therapy.
You say that he’s being transparent with his phone and internet which is good, but as you said, it isn’t foolproof. Is he expecting you to police him and fear of getting caught to keep him on the straight and narrow? This isn’t your job. Do you want a partner or do you want to be the mom/police/hall monitor?
You don’t need to have an answer to these questions right now, but I think you should definitely put getting immediate evaluation and counseling by a professional in diagnosing/treating potential addiction on his to-do list and then step back and see if he follows through. Couples counseling just isn’t the right move this early. You both need to work on your own healing individually, and you need some time to stabilize, begin to heal yourself, and figure out what you want to do next.
It’s a tough call on telling family and friends, but most here would recommend that having at least one person who has your back and can provide in person support is really helpful. We all have wrestled with dealing with the opinions and judgement of friends/family, and yes, even protecting the WS who has devastated us or, more often, protecting our kids. If there is someone that you trust to provide support and honest supportive input, it can be a really blessing.
You’ll get a lot of advice, support and common ground here. We generally say that everyone here gets it, but we don’t all have exactly the same experiences. Some of us found infidelity to be a deal breaker. Some of us had cheating spouses who didn’t have it in them to do the hard work to become safe partners. And some of us tried or are trying to reconcile, some successfully.
So you will hear advice all over the board. Definitely take what you need and leave the rest, knowing that everyone here comes from a place of wanting to help, support and share the hard wisdom that has come from being forced into an experience we never wanted or deserved.
You will find great support and community here. I’m sorry that you had to join this group. Wishing you and your kids peace.