Your situation is on the unique side for this board, but not too unique for the court system.
My guess, and this is only a guess, is that your wife is addicted to drugs and has been for some time. It's either that, or some form of a mental breakdown.
I remember the early days of your story, and that it struck you out of left field. When I went through the whole infidelity thing, it struck me out of left field too. However, yours has always had some sort of a mental health or drug addiction angle. Call it experience, I guess.
When I say that you have to be the sane parent, I mean it with a huge emphasis. When situations like this popup, the courts cannot put your kids with the WW. It's either you, or the foster care system. And, I won't give you some of the horror stories that come out of that system. There are some sterling parents in that system, and there are some terrible ones.
You are absolutely correct - you want your WW to have a relationship with her children. You want them to have access to their mother. You want a stable co-parenting relationship with her, for your kid's sake. You are correct there. It would also be nice to have weeks where you can focus on you - I get that.
Right now though, your WW is spiraling into a life that I cannot fathom, but I have seen happen. I cannot tell if it's a drug addiction that has exploded, a mental health issue, or both.
What I can tell you is that - if either issue is present - then you have a long road to go down.
If this is a drug addiction, then you should know that this will be a rather constant issue. Drug addiction is notoriously hard to escape, and even harder when you have lost most of what makes life worth living. I have the upmost respect for those that were able to do the work and escape it. However, it often takes a few stumbles. Your EXWW will probably have to attend in-patient rehab if she has any hope of getting better (assuming this is the primary issue), and, even then, it's unlikely that the first time is the charm.
If this is a mental health issue - such as a period of bi-polar mania or an organic situation like a brain tumor - it is again a long slog.
There's no easy way to say this, but it bears repeating that you have to be the sane parent.
To put it bluntly, when it comes to her you need to:
1.) Cease responding to her contacts unless it is about the children.
2.) Make sure any interactions are recorded and preferably you have witnesses that can testify.
3.) Keep a written record of everything you do on a daily basis so if you're accused of something you have a way to go back and say where you were one day.
When it comes to your kids, like to said before, you need to get them in therapy. I know. It SUCKS right now. You're holding down a job and being a full time parent. But, they need something to help process what just happened.
Imagine what it would be like to be one of your kids. A few months ago you had a happy and safe home with the parents you'd known all your life. Now, your parents are separated, they've lost their rooms and home, mom has gone incredibly crazy, and they've heard or witnessed a drug addicted scripture spewing possible gang member possibly try to kill their mother.
They need you. They need help. They cannot afford to lose you.
Right now, my guess is that you want to curl up and lick your wounds. You want to have fun with your new girlfriend. You want to move on from this mess and find happiness.
Your kids, on the other hand, have been traumatized more than you know. This is an incredibly sad story, and you are incredibly strong based on what you have done already, but you need to continue to focus on them.
The ideal is that mom gets better and she can be in their lives in a safe, supportive way. My prediction is that it will not happen for some time, and, if it does, it will be on a limited basis.
It's not fair, but your kids need you more than anyone else and you're the only one left standing. You're strong. You can do this. I know it sucks, but it will also be beautiful looking back.
I feel for you man.
Again, not legal advice. Talk to your lawyer and follow only their advice.