Because there are a number of states that require having licenses and shit for even a disassembled handgun in a locked box.
Seems a lot of her shit is boomer fudd tier guns. No high cap mags or "assault weapons." The
Firearm Owners Protection Act should help as she's passing through, but doesn't protect hotel/overnight stays as I understand it. For her to get diddled by the law, majorly, would require her vehicle to get searched, which would require reasonable articulable suspicion. Very unlikely concern imo.
Google maps showing me a route from SC to Oregon shows three main ways to get there and they only have one route passing through Illinois, which has the worst gun laws of any of the states she's likely to pass through on her way there, but they do have Peaceable journey laws on the books. Idaho, Utah, Wyoming, Nebraska, Kansas, Missouri, Arkansas, Mississippi, Alabama, Tennessee, Georgia are all better state gun law wise and should pose little to no risk of fucking over Pips. Hell, you gotta remember 27 states have permitless concealed carry now.
*this is all assuming a direct route
To check your state, or surrounding states, here's a good couple links.
en.wikipedia.org
*edit again, didn't even touch on it as it's so unlikely, but if Pippa does have a CCW in SC, 25 states recognize that as a valid form of CCW in their state. For her trip only CO, IL, and OR don't recognize it as a valid CCW.