Hi msk99, so sorry this nightmare has become your reality.
Please hear and believe that things will not stay this way, you won't keep feeling the way you are right now. I know that seems unlikely from where you are at the moment. You will be told over and over that it gets better, and it does, not the same as before granted, everything will be different - but which ever path your relationship takes, it will be better than how you are feeling right now.
So, you wife is resorting to blame and justification for her disastrous choices, as you've been told already, despite what she says drove her to it, her affair is not your fault, not in any way, shape or form.
As for her AP having no share of the blame, well, he choose to have a relationship with a married woman, shame on him. Her comment just shows where her head is at at the moment, that and her comment that the kids would be ok with divorce, unfortunately her focus is more on him and her, rather than you, your family and your marriage.
It's not unusual at all for a WS to "hide" behind words, calling their affair a "friendship" is so disrespectful,I would call her on it every time if I was you. Don't let her hide, stick to reality and call like it is, especially seeing as she seems unwilling to commit to stopping contact with the AP.
Use the 180 to make yourself stronger, that's it's purpose, if it helps your WS to come out of the fantasy land she's in right now, great, if not, it will help you focus on what you need going forward. A hard version would be to talk about kids and finances only, let her feel a little of what life would be like without your support, hopefully she'll wake up very quickly and you won't need to go this far.
As for telling others, yes the AP's wife definitely, but if reconciliation is your goal, limit it to those who will be supportive of your marriage for now, once it's out there you can't control how far it goes.
Your wife is not the woman you knew right now, I hope she comes back, but you and the kids will be ok, regardless.
Take care, thinking of you.