Now for my interpretation of this scene.
Car is symbolic of the lives of Rishabala. RK is the driver of their lives. He gets to make the decisions and dictates where it is going. Madhu is at a point where she doesn't mind him taking charge but retains her own dignity. She would not go out of the way fawning over him although she deeply loves him. Now RK is used to a lot of adulation and wants his wife to be his biggest fan. He doesn't know that she is already his biggest fan, only she is a fan of the man and not the actor. He had tested the strength of her love by asking her to leave everything and follow him. She hesitated and he misunderstood her. Thankfully he got back his senses soon and understood her love and in setting out to test her love, he has taken his focus off his life and devoted his entire attention to her, much like how he took his eyes off the road and concentrated on her till she was forced to declare she really is his fan. In the meantime their lives (the car) has gone out of control and he had to bring it to a grinding halt. This would result in him facing disrepute (the blackening of the face) which will affect Madhu also. In their effort to rebuild their lives, it would be Madhu who would take on RK's profession and put their lives back in order.