I really hate this discussion. There is so much paranoia and what if's going on. We don't even have enough info from the opening post - for instance, how do you want to bring the pistol? For self protection along the trip or just move it to the new location? Where is the move going to be to? If you just want to move the gun, not have it readily available for self protection along the trip, it is very easy.
Here's the simple answer with out all the bull crud:
18 USC 926A:
Notwithstanding any other provision of any law or any rule or regulation of a State or any political subdivision thereof, any person who is not otherwise prohibited by this chapter from transporting, shipping, or receiving a firearm shall be entitled to transport a firearm for any lawful purpose from any place where he may lawfully possess and carry such firearm to any other place where he may lawfully possess and carry such firearm if, during such transportation the firearm is unloaded, and neither the firearm nor any ammunition being transported is readily accessible or is directly accessible from the passenger compartment of such transporting vehicle: Provided, That in the case of a vehicle without a compartment separate from the driver’s compartment the firearm or ammunition shall be contained in a locked container other than the glove compartment or console.
Broken down:
1. Can you possess the gun at your origin and at your destination? You will have to research the laws for the state you are moving to to determine legal possession there. Tell me what state, I will look it up for you.
2. Unload the gun. If you are driving a car with a trunk, lock the unloaded gun in the trunk with any ammo you are taking with you. That is all you have to do. You do not have to seperate the ammo from the gun, you do not have to lock the gun in a case, you do not have to disassemble the gun, you do not have to unload magazines. You only have to unload the gun and lock the gun and the ammo in the trunk.
3. If the vehicle does not have a trunk, the gun must be unloaded and locked in a case, again along with the ammo. I would put the locked case wherever you are going to put your other luggage in the car without a trunk. Like the law above says, you don't want it in the glovebox or console. As far back as possible, as far away from the occupants of the vehicle is best.
4. IMPORTANT! The object is not to seperate the gun from the ammo according to the law. The object is to seperate both the gun and the ammo from the occupants of the vehicle. If you have the gun locked in the trunk and a box of ammo in the passenger compartment, then you are ILLEGAL because the ammo is not seperated from the occupants.
5. When you stop at a motel or wherever, simply carry the guns/ammo, preferably in a case, into the motel room if you desire.
6. If you are stopped for any reason, you DO NOT need to inform the police of the weapon, if transported according to FOPA above. You might want to have a printed copy of FOPA available with your registration/insurance. I have NEVER EVER been asked if there are firearms in a vehicle during a routine traffic stop. DO NOT volunteer such information, it is not required. If by some minute chance you are asked, state that you have an unloaded gun, stored (wherever), being transported according to the Firearms Owners Protection Act. You DO NOT have to consent to a search, because at this point there is no reasonable cause to believe that you are breaking any law. If the cop can see a box of ammo unsecured in the passenger compartment, then you are out of luck.
This is REALLY REALLY SIMPLE. I moved from Oklahoma to Washington State with a Uhaul trailer. Locked in the Uhaul trailer was no less than 13 weapons and no less then 3,000 rounds of ammo along with 2,000 to 3,000 primers and 30+ lbs of gun powder. Both my wife and I chose to remain armed for as much of the trip as we could, so we researched each states' law and conformed to each states' law regarding open carry. If we did not desire to be armed, we would not have had to do that, just lock the dang gun up in the trunk and don't worry one bit about it.