I have just re-read your posts and there seems to be quite a bit of confusion over what this is. Not a relationship, but to be kept monogamous? That sounds a bit contradictory and unclear and destined for disaster.
From what you say, she has been quite honest and up-front with you, telling you quite early on that she is attracted to someone else and wants to be non-monogamous. That is very different from going behind your back and reneging on any agreement you might have. It gives you the choice of being in a non-monogamous relationship with her or not. You might not like her approach, but she has not actually done anything wrong. So, I think, from reading your posts, she has taken responsibility.
You have only been seeing each other for a month, that is hardly any time at all to really get to grips what you want from each other and perhaps she is exploring her feelings. Perhaps it is just a friendship that got a bit physical and now she is looking for a way out, who knows.
I still think you need to decide what you want, both in terms of a relationship with her, but also with your long term friendship.
Sometimes we just need to walk away.