I'm very sorry that you've experienced being betrayed. As awful as you feel now, you can survive and thrive.
Fear of D
I strongly recommend the fear-vs-reality thread in the Divorce/Separation forum - https://survivinginfidelity.com/topics/497843/fear-vs-reality/.
Kids
Unfortunately, I watched our grandson go through his parents' D. It's been a tough 6 years watching him, and I'm sure it's been more difficult for him. But-but-but: if his parents had stayed together, it would have been much more difficult for all of them. He's 14 now doing very well in a demanding high school, making friends, growing. Nothing will remove the pain he feels unless he does it himself, so he'll probably seek therapy in 5-10 years, but he'd be sunk much more deeply in pain if his parents had continued to live together.
Kids can recover. They tend to be even more resilient than adults.
Shame
You have nothing to be ashamed of. Your H is the one who couldn't keep up his side of the M contract. I, too, urge you to seek support from your family, if you think they will support you.
Pain
The SI rule of thumb is that it takes 2-5 years to heal - IOW, 2-5 years to process the pain out of your body. As you process the pain, you'll probably start feeling better - very slowly at first, but the improvement accelerates as you continue to process pain. But first you need to hit your rock bottom. A lot of us do that midway through the 1st year after 'd-day' plus or minus some months. I personally spent about 6 months of the 1st year before I started noticing the return of joy. YMMV.
Reconciliation
To R, both of you need to be willing to do the necessary work. That is, IMO: 1) BS processes the pain out of their body; 2) the WS changes from betrayer to good partner. Both are necessary. If either one is missing, R will not work.
So far, you report a WS who is not willing to do any work. I think R isn't possible at this point - but he may change.
In any case, for R to succeed, you heal you. Your WS heals himself. Together you heal your M.
That means you need to do your work - processing your pain. If you do that, rather than wait for your H to help you heal, you'll come out of this stronger and wiser - and ready for a good relationship with someone, if that's what you want.
The same goes for your H - if he changes from betrayer to good partner, he'll be stronger and wiser and ready for a new relationship. If he doesn't do the necessary work, he'll continue to look outside himself for something that can come only from inside himself.
Encouragement
You can heal, Marie. Your best bet is to invest in yourself. Let yourself feel. Take the time you need to make decisions. You have a whole new world of options open to you. The pain of being betrayed may seem like and giant, unavoidable, perpetual obstacle right now, but it's temporary. As you heal you'll see the obstacle diminish and, eventually, disappear.