Road trip with my shotgun in car from CA to TN?

[CHUNDER]

Takin a roadie to Bristol Nascar race in March on HWY 40 from CA to TN. I plan on bringin my shotgun with me in my truck for protection on the road and while camping.
My shotgun has an 18barrel and has an overall length over 31 inches.
The shotgun will have a trigger lock and separate locked ammo box.
What else do I need to know since I have never travelled cross state lines with my shotgun. Also what do you do if you get stopped by the law?
FYI---HWY 40 goes thru these states-AZ, NM, TX, OK, AR, TN. Thanks to all in advance!
ps- I am the legal owner of the shotgun, and I am NOT a felon!
I will have the weapon ready for use at my campsite. I will NOT travel with it loaded!