I feel for you, i really do.
On the one hand you could walk away, but i get the feeling that the little girl would be just as tough to walk away from if not tougher than the life you have left behind.
Is it worth meeting her, but somewhere neutral? Sometimes these things are done in comfort zones - she feels comfy in her own place and therfore acts differently. Perhaps that would remove some of the false front that she is obviously showing. it may make it clearer for you to see through any lies she throws out. I think you need to explain from your point of view how much she has hurt you and why. If its too tough to tell her, perhaps write to her instead?
I think for your own sake, you need to understand why she has acted like this. It will allow you to see if there is a future here and thus allow you to plan your next move. If it becomes clear that she is messing with you, then you need to be brave and cut all ties. If you dont it will only hurt you more in the long run, and could also have an effect on the little girl (a point I think she needs reminding of too). If she has made a genuine mistake then you need to know why she felt the need to sleep with someone else - was it something you did, or something you can work on?
The OD is a bad idea. I work in the NHS and have an understanding of such things as well as seeing a close friend attempt it in the past. Its not pretty and hardly ever works, leading to long term health issues. Please dont do this. Your life could change for the good just as quickly as it has changed for the worst and its not worth making decisions based on 'recent' events. I think you owe it to yourself to try and fight through this if you can, if nothing else it will lead to answers as to why this has happened.
I wish you luck from the bottom of my heart. We are here for you if you need to talk further.