Is it permissible to walk and ride in a car home while being in a state of impurity after urinating at the end of the school day?

If it is possible for you to remove the impurity as soon as you are afflicted with it, that is best, for a Muslim is enjoined to be clean. However, there is no harm in going home before removing it, if you did not intentionally become afflicted with it. You must be careful not to soil the car if the urine is still wet and the car does not belong to you.