We travel frequently from upstate NY to Fla by car. Have FL non-resident permit, which makes carry easier in most states, however there are a few states that do not recognize either. Federal statute provides for legal transport through states which do not recognize your permit(s), as long as you are legal in your home state and they are securely transported.
You have to decide if you want to stop...unload...lock pistol and ammo in separate containers where not permitted...then stop...reload....continue to carry where permitted.... this becomes a hassle, especially now that PA does not honor FL non-res permit. If weather was good through the Appalachians, we had no problem most of the way, taking a route through PA, WV, etc. But, if weather is bad in Western PA and better to the east, we would head toward Harrisburg then south. So we could carry to the Maryland border but had to get out, lock them up separate from ammo, drive approx. 10 minutes, leave MD, get them out... travel to SC border...get out...lock them up...you get the picture. Now, we have to lock them up at PA border until we leave MD and can carry until the SC border.
Basically, you need to measure your risk of running into BG or uninformed LEO versus the hassle of unloading/reloading.
Additionally, you have to make sure you are in compliance with each state's regulations as well....Must Inform...carry in restaurant/bar...Do "no weapons" signs carry power of law?...etc...etc...etc. Better have copies of regs for each state you pass through with you (ie. handgunlaw US), which give good synopsis of each state's laws because, unless you have a photographic memory, you can't remember all of them....plus, don't expect each LEO to know their own handgun laws. They may just "arrest now" and "Read law later"!
We've found that other than stopping a couple times for gas, it's a toss-up on whether we simply lock them up for the entire trip or do the stop/start thing. We take time of day, which route we're traveling(plus weather) into account when deciding to carry or lock.
Either way, we do take them into the hotel if we stop overnight (and load them), and figure if someone breaks into the car, they can have my clothes, but they can't have my guns.