Quoted:
"Loaded" in Virginia= round in the chamber.
In theory you should be fine, however there are some technicalities that an "exuberant" LEO could use to nail you under the concealed weapons laws. The hunting laws don't apply because they only address loaded weapons.
What I'd be more worried about is someone having a problem with the rifle constituting a "hidden from common observation" concealed weapon that wasn't covered by your permit (IOW,not a handgun).
I suspect in almost every rural jurisdiction, that you'd be fine with an unloaded rifle in the seat next to you,with mag engaged in the rifle. However in a big city, with an AR shoved down next to the passenger seat and a loaded mag engaged (which your fellow drivers would not be able to see), you might end up getting hassled.
Now,if you're talking about an unloaded long gun with an engaged mag sitting in the trunk our out of reach, then you'd be fine in any jurisdiction.
PS,
Do you know where in VA law a loaded gun is defined?
I had always taken loaded gun to mean in the chamber, in an attached magazine such as a tubular magazine or with a loaded removable magazine inserted in the gun.
I was so sure you were wrong that I started searching VA laws and DGIF regulations looking for the definition of a loaded gun, and I can't find one.
I'm wondering if I can't find it because it is defined in case law.