Lots of comments, but still a little confusing with so many different methods. So, we stopped at a National RV dealer yesterday and talked to service. They said not to use Liquid Plummern as it creates heat (I looked at the info on a bottle and it said safe for septic systems and PVC). He said I could use a snake, but not the ones with the barbs. He also suggested the hose solution and recommended short bursts. He also showed us a solution that can be used to help clear the drain. They also had a solution which, after the drain is clear, you can use and it sort of 'oils' the drain to help keep it clear.
So, we're going to try the hose method. He said to have the gray water hooked up to the sewer before doing it. Then, we're going to get some of that other stuff that will keep it 'oiled' and also get a small screen for the drain which will catch the hair before it goes down the drain
<font color="#0000ff">George Eldridge