The statements aren’t that natural or precise, depending on who ‘they’ are, how many cars the family has, and who drives. They drive their parents’ car(s) to school. They drive one of their family’s cars to school. They drive a family car to school. Their parents drive/take them to school.

Your sentences say that the students drive themselves to school using a car that belongs to their parents. Is that what you meant to say? If that is not what you meant to say then both sentences are wrong. The first sentence is correct. I would prefer "car" since a student can only drive one car, but "cars" is not wrong because all the parents together have many cars. The second is also correct, but several improvements could be made: Use singular "car" "in", "with", or "using" their parents' car

Their parents take them to school, They drive thier parent's car to school. These are the correct choices.