We go to the SW annually. Via Hwy 97 to 395 to L.A., thence to Tucson (formerly Flag), then on to Gallup or back via Las Vegas. From Gallup up through Boulder and back. Or maybe to Yellowstone and back I-90. Or maybe down the Coast Highway to Monterey to SoCal. Al;l depends on which relatives we are visiting.
First, if there is time get CCW permits for as many states as you can. I have OR, UT, & WA. Wife has WA and UT. Check a reciprocity map and determine which are best. Carry a copy of the map with you! I keep it in a folder with addresses, reservations, etc. For us on our trips, my permits cover WA, OR, NV (not needed), UT, AZ (not needed), WY, MT, ID. We have a locking gun case that is attached by cable to the front seats in our 4Runner. We stop for gas in a border town and lock the pistol(s) if necessary. Be sure you know if you have to declare you are carrying if stopped. State laws vary. I was once stopped in Utah for speeding and told the trooper I was returning from an elk hunt and had a 6x7 in the camper, frozen and packed. He asked if I had any firearms in the car (???

). He said I was getting a ticket anyway, so I said "No, I strangled it"!
Utah permit: Requires a safety class (can be done locally), fingerprints and photo. Application can be done on-line.
Oregon Permit: Weird regs! Counties on the border CAN issue non-resident permits to adjacent state IF there is reciprocity. In actuality,very few do! Ironically, Multnomah (Portland) does. You need to send a justification letter with your application, take an Oregon Sheriffs' safety exam on-line, make an appointment for photo and fingerprints in Portland, have it done. If you are clear, you get an e-mail stating it is in the mail.
Important: If stopped, I roll down the window, place my hands on the steering wheel, and inform the officer that (a) I have a permit, (b) am carrying &, (c) how would HE like to proceed? The last time I was stopped the officer said thanks for telling him and he was always happy to see an upright citizen carrying. A couple of times they have asked what I was carrying and why I chose that particular weapon.