If you don't believe that she is cheating then you move on with that knowledge. You are exactly right, there is no way to prove a negative.
You run your race, sweetie.
I agree with Denver that, in fact, things are toxic, though. I'm not saying that you are contributing to it. But your W has really has been angry. Ultimately, whether you stay or go is up to you. But you need to see the situation for what it is.
I know you are struggling and in pain. I'm so sorry for that. Even if you do separate, please know that it is not the end. In fact, it could be a new beginning. And if you don't separate, that's fine, too. But you really need to find a way to diffuse the angry. I really think that you've done quite a lot already. I don't know if its just time that will take care of the rest. But be mindful of what you are trying to accomplish and what you feel will get you to that end.