So I am just some internet stranger without full context - but I gotta say... the way you describe it, it sounds like you should break it off. To review:
- Started the relationship by accident
- Had 2 more kids even though she didn't want to have sex with you
- She refuses to go to therapy
- The two of you are officially separated
- She tells you to find someone else
- She has a history of being violent/aggressive with you and your kids
- She has stated she never wants a relationship or sex again
- Your kids are losing out on the opportunity to see a healthy relationship
- You fear this state of affairs will last the rest of your life
- You fear she will hurt your kids
- You are not happy
Again, I am an internet stranger working without full context. But I would say you should lawyer up, completely split up and move out, and move on with your life. Get the lawyer to figure out the best way to ensure custody of your kids beforehand, then give her an ultimatum - get help, or you are leaving and either taking the kids or going to court to take as much guardianship as possible.
I'm not saying she has no redeeming qualities or that the time the two of you shared wasn't special. But it sounds like she can be mean, aggressive, and possibly violent, like she doesn't consider herself to be in a relationship with you and doesn't want to, and that she is unwilling to try to change and probably won't. And this state of affairs is having a negative impact on both you and your kids.
Meanwhile, by sticking with her, you are giving up the opportunity to find someone else who does want to be in a relationship with you, who can model a healthy relationship, and who will make you happy.