Federal law does NOT require the gun to be separated from the ammo. The law requires both the gun and the ammo to be separated from occupants of the vehicle, but not from each other.
Federal law allows you to transport your guns in your vehicle as long as it is unloaded and in a locked case and separated from the ammunition, and if you don't make any unnecessary stops between your starting location and your end location.
TITLE 18--CRIMES AND CRIMINAL PROCEDURE
Sec. 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.