OP, I completely get how repulsive and horrifying the idea of your DC going through parental divorce, having two homes, and perhaps meeting a STBEH's new partner in the future, is to you.
You are going through marriage break up; it's something that's happening to you and your kids, and it's not your fault. Meet it head on as you would illness, redundancy, flood in the home etc. At the moment it isn't a happy home and that will be affecting your DC no matter your efforts; the version you want, where it's a happy two parent family, is not an option now and very sadly you have to accept that and let it go.
I think the final part of letting go of STBEH and your marriage, is accepting him with someone else. It might feel impossible at the moment, but honestly one day you won't give a fig. You'll just feel sorry for her. I promise that day will come.
You sound like you are grieving your past relationship, and the life you thought you would have. That's to be expected and therapy could help; time definitely will.
You can allow yourself to have these emotions, but you can also use your rational thought to take your next steps. Your kids will be ok. You will be ok. This is the hardest bit and it will pass. Let your family help you and take your next steps 💐