I would also give the thumbs up for carting over motocross when it comes to my child.
I would say that he has a better chance breaking a arm when riding his BMX bike like a maniac than racing a cart. They are very tight gripped on the road surface and will take a crazy move to make it fall over, if it even is possible. Find out the classes, maybe you can share one cart. He drives junior class and you drive senior class. Or something like that.