First I would call Stephen Foster State Park to see if they have a water fill area. Usually there's one at the dump station and no, you never use the hose at the dump itself. When there's potable water at a dump station it will be found a distance from the actual dumping spots. It will be marked 'potable' and it will be perfectly safe to use in your tank.
Also, you just might have water at your site and don't realize it. Ask the park.
When you're ready to leave the state park for your next stop, fill up again and you'll be all set. Have a great trip!