What is the ruling on riding in a car that is thought to have become impure with urine, and is obsessive doubt about its purity considered to affect prayer, clothing, and social interaction?

The questioner is afflicted with waswasah (whispering of Satan), and the cure for waswasah is to completely disregard it. The default state of things is purity; thus, the car is pure until proven otherwise. The default state of a Muslim is truthfulness, so the mother and sister must be believed if they state the car is pure, unless there is evidence of their untruthfulness. It is not permissible to contend with one's mother. Even if the car was impure, the incident is old, and if the impurity dries and is touched by something dry, it does not transfer the impurity.