Parking RV overnight at trailheads within national parks?

No...for national parks you cannot leave your RV at a trailhead or leave it unattended overnight.

If you're backpacking, you need a permit and at that time they will tell you where to park. You can't just go out on your own to backpack in a national park.

Also, for some trails you can't even get a backpacking permit for the same day. Sometimes you have to get it in advance.

It's best to pick your park and contact the backcountry office before you go so you're not disappointed.