If it were me, I would have to tell him that I refuse to do anything that enables his A with the OW. That includes driving him to the airport so he can go be with her. Now, I could get down with the best of them and even refuse to do his laundry to enable him to have clean shorts for his "weekend" with OW.......see what I'm trying to say? Anything........ANYTHING at all that is helping him, or to make it nicer to have an A with OW, I would refuse to aid the situation.
I don't think you should "help him" by covering up his adulterous affair. I wouldn't say anything in front of the children, but I don't think you should feel as if you could not call it what it is.....and let him deal with the effects. If he doesn't like it.....then too bad!
He told you not to count on him being around, so that is exactly how I would live. Go about your business and living life as if he wasn't going to be around. How would you live your life if that were true? Think about it and then drop the emotional rope that you have tied to him and set him free. Treat him as if he is no more special (or worse) to you than anyone else. I think he is making a very obvious statement to you and he has already gone over any marital "lines", but as Puppy said, call his hand on things when he openly disrespects you. Don't get into an argument or a R talk.....simply leave the room or walk away. That makes a statement to him!
You should not feel that you have to explain your "plans" when he has clearly let it be known that he has no interest in joining his family. Be vague and say as few words as possible. Get out of that habit of giving a play by play of everything you do or plan to do.
Different people have different points of view about contacting the OW and busting the affair. If you do decide to do this, don't expect your H to quietly accept you contacting "his" OW. I can't tell you what the outcome would be about the A, but I can tell you that he will not be ready to fall into your arms. Think long and hard before you do any action about contacting OW.
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!