In a marriage, cars are normally titled in the husband and wife’s names. In Florida, if you cause an accident, then you are responsible for any damages that result. However, if your spouse is on the car, then s/he is also responsible for any damages that result because you are both owners of the vehicle. So, if you get a divorce in Florida and you go through the equitable distribution of assets, meaning that you both take equal shares of your assets, property, etc. and one car goes to you and the other to your (ex)spouse, it does not change the fact that you are responsible if s/he gets in an accident.
If you take one car and your (ex)spouse takes the other, then make certain to get titles switched into your individual names. You would actually need to do a transfer of title and get it registered with the State of Florida. Once that is done, you also want to get the vehicle insurance changed.
Vehicles are not the only property that has title. If you are going through a divorce, you should consult with an experienced family law/divorce attorney. A Florida lawyer can help you understand your rights and how to best move forward with property division including your home, bank accounts, retirement and, of course, vehicles.