I live in New York and both my wife and I have separate cars, both in her name. Our divorce is pending, can she claim I stole her car if I regularly d

As you have probably learned in life, anyone can do anything if they get a bug up their behind. In order to prevent the situation you described, you should seek an interim court order allowing you each exclusive use of your respective cars pending resolution of the divorce. That will prevent her from reporting the car stolen because if she did, she would be violating a court order.