There are a lot of laws in different states and locals. When transporting guns across state lines, there is a federal law which supercedes all local laws, or at least it says it does. Here is the exact law. This has been Federal law since 1968.
Sec 18 USC 926A. Interstate transportation of firearms.
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.
This means that you can carry a gun in your car through any state in the union as long as it is carried according to this statute. I am not sure about D.C..
Flash, in your jeep you can carry your firearm unloaded in a locked box, because it is one of those vehicles noted in the federal statute that does not have a trunk. To be safe, put both gun and ammo in separate locked boxes (like a small locked tool box.)
You can even carry unloaded guns through National Parks, although signs often say "No Firearms". Here is a copy of the law pertaining to firearms in the National Parks.
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Note the separated section below.
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Chapter 1-National Park Service, Dept. of the Interior. Part 2-Resource Protection, Public Use and Recreation:
Section 2.4 Weapons, Traps, and Nets: (a)(1) Except as otherwise provided in this section and parts 7 (special regulations),and 13 (Alaska regulations), the following are prohibited: Possessing a weapon, trap or net (ii) Carrying a weapon, trap or net (iii) Using a weapon, trap or net (2) Weapons, traps ornets may be carried, possessed or used: (i) At designated times and locations in park areas where: (A) The taking of wildlife is authorized by law in accordance with Sec. 2.2 of this chapter: (B) The taking of fish is authorized by law in accordance with Sec. 2.3 of this part. (ii) When used for target practice at designated times and at facilities or locations designed and constructed specifically for this purpose and designated pursuant to special regulations. (iii) Within a residential dwelling. For purposes of this subparagraph only, the term "residential dwelling" means a fixed housing structure which is either the principal residence of its occupants, or is occupied on a regular and recurring basis by its occupants as an alternate residence or vacation home.
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(3)Traps, nets and unloaded weapons may be possessed within a temporary lodging or mechanical mode of conveyance when such implements are rendered temporarily inoperable or are packed, cased or stored in a manner that will prevent their ready use.
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(b) Carrying or possessing a loaded weapon in a motor vehicle, vessel or other mode of transportation is prohibited, except that carrying or possessing a loaded weapon in a vessel is allowed when such vessel is not being propelled by machinery and is used as a shooting platform in accordance with Federal and State law. (c) The use of a weapon, trap or net in a manner that endangers persons or property is prohibited. (d) The superintendent may issue a permit to carry or possess a weapon, trap or net under the following circumstances: (1) When necessary to support research activities conducted in accordance with Sec. 2.5 (2) To carry firearms for persons in charge of pack trains or saddle horses for emergency use. (3) For employees, agents or cooperating officials in the performance of their official duties. (4) To provide access to otherwise inaccessible lands or waters contiguous to a park area when other means of access are otherwise impracticable or impossible. Violation of the terms and conditions of a permit issued pursuant to this paragraph is prohibited and may result in the suspension or revocation of the permit. (e) Authorized Federal, State and local law enforcement officer may carry firearms in the performance of their official duties. (f) The carrying or possession of a weapon, trap or net in violation of applicable Federal and State laws is prohibited. (g) The regulations contained in this section apply, regardless of land ownership, on all lands and waters within a park area that are under the legislative jurisdiction of the United States. {48 FR 30282, June 30, 1983, as amended at 49 FR 18450, April 30, 1984; 52 FR 35240, September 18, 1987)
These laws are good to know now that traveling and vacation season is upon us. Fortunately my permit is recognized by many states. I have found that by also obtaining out of state permits from FL and UT I can legally carry in about 23 states including all the states I travel to on a regular basis.
It can be helpful to print and carry a copy of these Federal laws with you while traveling. If you are stopped and the gun becomes an issue, most officers will not press the issue if they are aware that the federal law is being followed.
I have even carried this way to the Canadian border. At the border, you must declare the firearm and surrender it to the Canadian border guards. They give you a receipt for the gun and you pick it up on your way out of the country. I have crossed at the NY / Canadian line this way with no problems.