It's the 'please' that convinces her. That is the key to unlocking what she hears in his voice, the edge of actual worry, of sentiment, and when it falls into place she sighs and walks back to the car.

Because she realizes what has been driving him and she caves. It's losing and she cannot help it.

"I will if you let me drive."

The fact that the worry is mutual doesn't make her feel any better.