Can I switch cars with my wife if the car is in both our names?

As a legal matter, since both the cars are marital property then you can possess and operate your spouse's vehicle and she can possess and operate yours. As a practical matter, however, if you take her car you are asking for trouble. Starting with her calling the police and accusing you of trespassing if you take it from her garage or driveway, seeking an injunction against you, seeking an interim distribution to have you ordered to return the car and later on down the road making a fuss in front of a judge over the fact that you took her vehicle, it is generally a bad idea to take property that you may have an ownership right to but is currently in the possession of the other party.