IMHO, you are handing this entire thing with an extreme amount of grace and class. I am so, so impressed with how strong you are and what a great mom you are.
Of COURSE it is hurtful and crazy-making to have her along in the car on exchanges, especially the day when he came at the crack of dawn just to go back home. In my sitch I spent some time thinking about this or a similar scenario, my children spending time with AP, and it was the one thing that completely made me lose my cool. I felt like my vision was literally being obscured, like this curtain of red rage was coming over me and making it impossible for me to think straight or breathe or even see. So you smiling, calm, being the sane decent human being and mom to S2 in this situation feels like superhuman strength to me.
And... I believe he is doing it SPECIFICALLY to make you feel badly. He is a narcissistic a-hole and is doing everything in his power to try to have an effect on you, your feelings, your behavior. He was used to being able to dictate your moods and feelings with his own and he is lashing out in every way he possibly can to feel he has power again over you. (And it says a lot about her that she is either mean or dumb enough to go along with him on this... I mean, think if the situations were reversed, and you happened to be dating someone who was in the middle of a D with a 2 year old child. I feel like I would completely remove myself from any interactions with the child at all until way down the line, let the dad have the time to bond alone with his child, and FFS NOT insert myself into the exchanges with the mom!!! What is wrong with these people??? Never mind, I know the answer.)
Anyway... I know you know this, but the only way to deal with him is to not. Don't let him see you flinch. Don't give him that power. Know that your reactions are normal and show that you are a human being with normal feelings, and it is OK to have all those feelings. And naming them and feeling them will help you to let them go.
S2 is YOUR son. And you are a great mom. Do everything you can to let what doesn't serve you go, embrace the zen, and focus fully on the time you get with S2.
Hang in there. You've got this.
Me (46) H (42) M:14 T:18, D9 & D11 4/19 - 12/19: series of escalating BDs 9/20 - present: R and piecing