Basically I said, that she had been going off on random days, coming home with no pattern for the kids to stick to, and the kids had begun noticing, and are generally really nervous and paying attention whenever she leaves the house, often they cry when she just goes to take out the trash etc - She said that was nonsense, and had nothing on it.
Hurt, I know it's a sucky situation and I do feel for you. But reading your posts I think you're trying to "guilt" her back by using the kids against her. One thing you need to understand is she is wayward, and the wayward's mindset is that this is all your fault. So when you try to guilt her, she is just thinking that you are being unfair/ mean/ vindictive. You've got to stop that. Be the rock and lighthouse.
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I said, that I had informed her earlier, that it would suit our situation, and our chances of having a solid foundation for working together in the future around our kids, if she moved out now.
Your kids are 1 and 3, at this point in their lives the "best" situation for them is both parents under the same roof. Believe me, things get a lot more complicated for kids when the parents live apart. Now I am not saying you should continue to put up with her crap, I'm just saying quit hiding behind the kids as an excuse. Her moving out is what YOU want, you don't need to offer her reasons and explanations. What reasons and explanations has she offered you for running off and banging OM?
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...and that I had no intentions of harming her, I just want whats best for our kids. She then got really mad, before she burst in tears and said "I am so afraid, I don't know what you are capable of any longer", meaning if I would take the kids away from her. I said "I have been nothing but gracious through all of this, and you having those thoughts shows me that you perceive things very different from me", I then said I thought of her as a great mother for her children, however this situation had stirred the pot, and she made some decisions at times, that was not in the kids best interest, according to me at least, and im sure she didn't see it that way. She didn't. She became angry, didn't want to talk about ANYTHING but kids, which is what we should be doing. I kinda accidentally talked a bit about how OM and her were being a thing for days, and then she would come home and try to eat cake, and it was wrong - thats why we needed this to end, by her moving out.
Clearly that convo went sideways in a hurry and stayed there. You just can't reason with a wayward, she will twist everything you say. So don't do it.