Can I sell the car and get my half of the money in a joint car ownership?

Who was awarded the car in the divorce judgment or Marital Settlement Agreement. If it was awarded to you, then you can insist that she sign the title over to you, and if she refuses, you can have her held in contempt. Generally, the motor vehicle people want the signatures of both owners, if the title says X OR Y. But that policy may have changed. Why not call them and find out? Remember that if the car is far away, you might not be able to deliver it to your buyer.

yes you can do that.

No, you cannot sell "half" the car with out disclosing the status of title to the buyer or you would be committing fraud. You would have to resolve the issue of possession of the car and sale. Most Judgment of Divorce don't leave a car titled in both parties names. I would carefully review the terms of your Judgment of Divorce. She may have committed fraud by not disclosing the appropriate names on title when she registered the car in another State.

I would like to have a little more details, but if you have a title of she or you that it may well be possible for you to sell the car and deliver clear title to the purchaser. On the other hand, if you are in the process of a divorce than the car, its title, and a value are all at issue in the divorce or action for separate maintenance. Self-help is extremely dangerous.