S.B.
I did daycare in my home.
The kids followed the rules and the schedule. Period.
I pretty much handled things without involving the parents as much as possible. If somebody had a grumpy afternoon, I just handled it and we got through it.
However, I did have one little girl whose dad was a single parent. I ended up having to tell him to find somewhere else for her. She was disruptive to the other kids. She wouldn't eat what the other kids ate, she wouldn't eat when the other kids ate. She didn't want to participate, do her homework or pick up after herself. She also had a very smart mouth, which I absolutely did not tolerate from my kids. The other kids followed the rules. It got to the point that it just wasn't worth it to me to have her, and her dad expected me to cater to her. That simply wasn't going to happen.
The dad called me a few times after that because he was in a pinch. Nobody would keep her for very long. I told him I was sorry, but I didn't have room for her.
I think you should be able to talk to the dad without anything crappy being relayed to his son about you or your son. Maybe the boy was told to straighten up and the boy didn't like it. You won't know unless you talk to the father. You can let the father know that if this continues, you will have to change the arrangement because it's not working out.
I've had to do it and it's not exactly fun, but if your life doesn't depend on this carpool situation, you don't have to put up with any of this. You might find someone else to carpool with. You might be able to adjust your work schedule. All I know is that things ran much more smoothely when it became obvious nothing was going to change and I couldn't accommodate a child who refused to go along. Things went back to being easy and happy for everyone.
Try talking to the dad, but don't be afraid to pull out if it's clear things aren't going to work.
You cannot tolerate bullying and your son being a target. It's that simple.
Best wishes.