Here is something to try to keep the cat from rushing the door. It was a great training aid for ours.
Get a can of compressed air made to clean keyboards. Keep it outside (if the biggest problem is upon entering the rv) and have another inside if it's going both ways. When you go to open the door, be ready to give them a squirt of air. Cats hate that sound and should back off immediately. It won't hurt them, just aim it away from their facers.
Do it every time, and soon they will not approach the door at all. If they start rushing the door again, start with a shot of air again, reminding them. As I said, it's worked great for my two cats. They now just move on when we go to open the door.
