He's been lucky. In my area, admittedly a suburban verging on urban area... If you're carrying a Bowie knife, dirk, machete, or like object, underneath the driver seat as you describe... He'd probably have been charged with carrying a concealed weapon. If you're coming back from hunting or something like that... put it in the trunk, the back of the car or wherever. The bottom line is simple; know where your going, and don't be a knucklehead if you've got dangerous stuff in the car, no matter how legitimately you've got it!Yeah a cousin of mine likes driving these old junker cars and also likes carrying a big Bowie knife in a sheath under his front seat. He has lots of stories about getting stopped in the outback of Montana and Wyoming and Idaho and other states and warning the cop about the Bowie knife under the seat while they're searching around for pot/meth and other drugs. LOL
He says they always do the same thing ... pull out the Bowie knife, put it on the front seat, rifle around the car, and then hand it back to him when they're done.
Returning to the original question... As I said -- broadly speaking, you're probably okay carrying almost any reasonable martial arts weapons to and from class, especially if they're being carried in a way that's not going to put them immediately to hand. Some items may be more restricted (like shuriken/throwing stars), but even those are likely to be tolerated if they're carried in a reasonable manner (case in a bag, for example) and aren't immediately available to an occupant of the car. Of course, my opinion here is just that, and NOT a substitute for appropriate professional legal guidance. It and $3 will get you a cup of coffee at Starbucks...
I just wouldn't carry wooden training weapons in a car for long periods, simply because the car is a crappy environment; I basically steamed a bend into a bo staff that way once...