Welcome to the best club you never wanted to join.
Your H is comfortable w/ his current situation, so something has to change - he is getting what he wants from you and her. That's not cool. Does that mean you D it could, but it also doesn't mean it happens tomorrow. This takes some time.
I would encourage you to read the healing library, do an over the phone consultation w/ an attorney. Get a good understanding of the differences between S and D, and what both look like for you, and what your financial situation would be for either.
As far as your H goes, if you are interested in attempting to rebuild and reconcile you need to show him you are unwilling to accept the status quo. Big actions from you will have some impact on him, but they will also give you some strength, and peace of mind. I remember that constant upset and turmoil I felt in the early days after Dday. It was awful. But when I finally found my voice and stood up for what I needed, and wanted, man did things change.
I would tell him he is no longer welcome in your home until he can prove he is NC, has a clean STD test, and has enrolled himself into therapy to understand why he threw it all away, and continues to not be sure on what he wants.
If you are done, then be done, call a couple of good attorneys, get some consults, and file. Tell him you will only communicate w/ him about financial stuff and things to do w/ the kids. Then do your best to stick to it.
Listen there isn't a right or wrong choice in this, but it is definitely a traumatic time, and you are normal to feel lost, hurt, heartbroken, overwhelmed, and also hopeful, and confused, especially if he is giving your drips and drops or what you need. That is why No contact and the 180 is such a powerful tool for you. It gives you some distance, and will prevent him from confusing you, and giving you what we refer to as the most powerful drug around - Hopeium. Hopeium is that little bit to make you doubt your decisions. Don't believe it, don't fall for it. He has chosen to lie to you, and abuse you (yes affiars are highly abusive) for 2 years. Not only did he do that, but he found someone closer to your kids ages, than yours to do it with. He is a broken person, and until that broken person is willing to own what he has done, there is no hope.
Figure out some boundaries. Set them, and know you stumble a few times, that's ok. We are here to support you no matter the path you choose.
Also stop worrying about "being alone". Being alone can be a really good thing. It can heal you and you are going to find a level of peace and happiness that you didn't know was possible as you navigate this shitstorm.
Now for the other things I tell every newbie. Go get full STD testing, that means a pelvic exam and bloodwork. No worries, the OB/GYN's office sees this all the time, they will be kind, and understanding. Find out that you are healthy.
Secondly when there if you are not sleeping or struggling w/ eating, talk to the Dr about it. A lot of us needed a little help to get through this, some of us took meds, some of us see a therapist, a lot of us do both. But it is time for you to make YOU your #1 priority.
I also want you to start doing something kind for yourself every single day. A long walk w/ your favorite tunes blaring, a hot bath, w/ a good book, and once a week do something really nice for yourself. Go get food from your favorite restaurant, go meet a friend (hopefully soon) for a few drinks or dinner. Get a new cut or color that is sassy and makes you feel strong. Rely on your network of friends and family to support and help you through this.
Keep reading here, keep posting. We will help you through it.
(((And Strength))))