I read into that that he said he'd like to be there when Paul comes, and you said you'd tell him when Paul gets there.
Your morning conversation implied that you'd talked to Paul about coming in the morning, but had not updated H. I read nothing more into that than a misunderstanding. You had actually not talked to Paul, but just assumed he was coming in the morning based on the conversation you did have. That would have been one thing to clear up right away -- "H, I haven't spoken to Paul again. I assume he's coming this morning. I know you said you wanted to be here, but I don't know what time he's coming. I can give you his number if you want to call him."
WRT the drama surrounding his dropoff request, my H would read things into my offers in the same way. My IC told me that is "crazymaking" -- you're attaching an interpretation to his words that may not be there at all. He could be talking while he was thinking versus trying to demonstrate the effort he would have to make.
The "assume the best intentions" strategy would suggest you should be grateful for the offer and accept it as such versus reading in sinister motives.
If H then later comes looking for payback, post about that. You assume he will, and maybe for good reason, but if you want help with your own communication dynamics, for now let's assume goodwill and let H prove otherwise, and then share that.
If you did let H take S to school and told him you appreciate it, that would be a deposit in his love tank. He would feel like a good provider, he would feel like a good husband. He would feel like a partner in S's care. That good feeling might foster a positive cycle to start spinning where he would do something else nice in anticipation of a positive or supportive response.
It's when a negative response comes when a positive one was expected that you're going to see him start keeping score and expecting reciprocity.
WRT putting H in the same situation my W put me in, I don't suggest it. All W had to do was tell me that she wasn't happy in the marriage and I would have taken action. The affair and divorce request were completely unnecessary if she wanted to see change. She said nothing and made no complaint until she said she wanted a divorce.
Accuray
Married 18, Together 20, Now Divorced M: 48, W: 50, D: 18, S: 16, D: 12 Bomb Dropped (EA, D): 7/13/11 Start Reconcile: 8/15/11 Bomb Dropped (EA, D): 5/1/2014 (Divorced) In a New Relationship: 3/2015