If the child falls asleep in the car and doesn't therefore nap in the afternoon and keeps all the other kids awake then it's very reasonable to ask her to keep him home as you have other kids to think if ....if I was a parent of one of the other kids and I had to pick up a miserable tired child at the end if my day I'd be less then impressed ..... Is there no way she can make the appts at the end of the day ? Don't feel bad you did the right thing