Pretty surprised at some of the responses here. I don't know how OP is meant to forgive and forget an emotional affair, how she's ever meant to trust this man again. I cannot understand drawing the line at sex, but not at undying bloody love. StBXH is IN LOVE with another woman - she has his heart - and it doesn't matter if she is even real or not. He was happy to indulge in that contact and set his wife and family to one side in order to cultivate that relationship. Why should OP ever subject herself to continuing a relationship with a man who is in love with somebody else?
Regardless of if he's physically slept with OW or not, he has every intention of doing so and absolutely would have done already, if given the opportunity. He's declared his undying love for another woman. He has no respect for his wife, her feelings, or the commitment he made to her, and no regard for the happiness or stability of his family. That is not a man she can trust with her heart or her future.
Staying in an unhappy marriage with no love, no respect, and no trust, just "for the kids", is a great way to mess with the kids' heads and teach them unhealthy lessons about love and relationships.
@OP I don't think you've done anything wrong or plan to do anything wrong. He doesn't deserve a face to face conversation imo, and apparently he prefers his relationships to be conducted digitally anyway. You do whatever you must do for yourself and your family.
It can't be easy having to play the strong, happy mum and go on as though everything is normal in front of the kids while dealing with this kind of betrayal and pain. You must be very strong! I'm so very sorry this happened to you, and I really wish you all the best. 