Why was the kid's homework in The Dude's car after it was stolen?

Larry did, in fact, steal The Dude's car.

Larry stole the car, and took it for a joy-ride, then abandoned it. The homework was in there simply because Larry wasn't terribly smart, and didn't seem to particularly care about getting caught.

The theft caused The Dude and Walter a great deal of stress simply because they had not yet realized that Lebowski had duped them. If Lebowski had actually given them the ransom money, then Larry would have been a likely candidate for where the money went, and therefore is a major plot point... up until we find out that the ransom money, and everything related to it, was in fact a red herring the whole time.