It’s important to know that you will not have a problem with conceal carry in your car in the state where you got your concealed carry permit. Where people run into problems is when they drive their car out of the issuing state where they got their permit. Always make sure the permit that you carry is valid in the state or locality in which you are driving. Also be aware that there are variations in the laws from one state to another or one locality to another concerning the way weapons are carried in your car. Make sure you know the law before you enter a different locality. If you know you're going to be entering a new area that has different laws about conceal carry, it is a good idea to print out the regulations concerning concealed carry from the website of the state that you're entering. Don’t assume the police officers in the state you're entering will be aware of the law. Do your research and don't get in trouble.
Source: Jorge Amselle, Gun Digest Shooter's Guide to Concealed Carry, Chapter 3, “Buying a Gun and Traveling with Its”, pp. 50-53