I don't think the teacher will throw the kid out even if the teacher does catch the kid being a brat, as long as the kid is not being actively/physically dangerous. The teacher needs the course fees.

Even as I prepare to type it, this sounds lame. Nonetheless, endure. How long is the Driver's Ed course, anyway? You can put up with the kid for that long even though you certainly shouldn't have to. Don't bring yourself down to his level.