Well B, I hate to say this but your reality has changed. With that you have to change with it.
First, why did you send the invitation pic in the first place?
What you have to do is accept you are now truly separated in emotion and body as she is out of town. You need to respect that, understand your marriage is over (in a figurative way), and focus on the realities of what has transpired. This doesn't mean your marriage is over, but rather you need to change your mindset to that point....lovingly. So no more relationship talk...acting as if you are married...etc. You need to change your perception to that of a single father. Also stop the thoughts of bringing up moving to her new area....That just creates stress for everyone.
As for finances....Start thinking of how to budget your life without her income...now. In the same breath....she has left the marriage...on her accord....So she should not be expecting financial help from you at this point either. Marriage provides certain securities...leaving the marriage should mean those securities end. Does that make sense?
Now in no way am I supporting going online to chat....or date...or anything like that. Your focus has to be very easy...You and the kids...Nothing else. You are a single parent now and that needs to be your only focus. So get out of me mode and into I am a parent mode. You will be better off in the long run.
As for the sudden switch....I honestly think there is some one in the picture. At this point her references to you cheating are being used to validate whatever she is doing. You just keep admitting, accepting, and validating that you did what you did when she brings it up.....but the truth my seat is that something else is going on or has. You do not control what she does with the fact you cheated. That is her choice.....You can only continue to work away from being that man.