Praise be to Allah the Lord of the Worlds.
There is no sin in a woman having driving lessons with a professional female instructor. Moreover, she isn`t considered sinful for driving her car to fulfill her daily needs, and since this is one of the lawful matters, it isn`t permissible to ban her from that. However, the woman should pick the right time and place for driving her car to avoid any harm, in addition to observing traffic rules and regulations. And Allah the Almighty Knows Best.