Check out the laws on the NRA website for how to transport in your vehicle. I am not a lawyer, but the way I understood it is that if you are just passing through, they cannot charge you with a felony (just talking about the gun in the car and not CC). Please do not take my word for it and please find out for yourself .
I will give you an example: In Washington D.C. all guns are illegal, but if I travel through it with my handgun in my car on the way to a range in the next state, then I have, really, broken no law. Although it is on the D.C. lawbooks that I had broken the law, the interpretations of the federal law is that the states cannot restrict interstate transportation of any firearm owned legally in the persons home state. D.C. has said that they will not pursue legal action against someone who travels through their city as long as you do not stop, even for gas.
You still have to check out the state laws to see how you are supposed to transport (IIRC). For instance, in Md you just have to have the gun in an enclosed holster and it has to be unloaded. Md has no law that says you have to have the gun in the trunk or that the ammo has to be unreachable (a cop may say different though, but that is the way I read the law). In N.Y. (IIRC) you have to have the gun disassembled, in a see through plastic container and in the trunk.
I assume that because you have to obey the transportation laws of each state, that whenever you get to a state line you have to change the way you have your gun. (i.e. move it from the glovebox to the trunk, take it off your hip and put it in a see through plastic container in the trunk, take it apart and put each part in ten different places in the car and have them all seperatly locked, etc.)