It sounds like you fill valve is leaking, in the bypass side.
In one position it sends water directly to you plumbing and does not fill your tank. The other position send it to you tank.
You should have a monitor that tells you when your tank is full, in the coach. They need to put one in the wet bay so you can tell without having to go into the coach.
If you let it fill to the point it flows out the gravity water fill port, it is too full and will slop out going down the road. If it get that full just run some into the gray tank, at the sink.
Your gray/black tank switch, if you have a flushing or rinsing system, sends water to either you gray or your black tank.
Fill your gray tank then fill your black tank. after connecting the sewer hose pull the black tank handle with the fresh water still entering the tank.
After it is empty continue to let it run for about five minutes. close the drain valve and let a few gallons go into the black tank.
Pull the gray tank valve and switch the fresh water flow into the gray tank. After emptying let it run for about five minutes. Close the valve and let a couple gallons go into the gray tank. Turn water off and disconnect.
Sorry if this doesn't fit but from you description this should cover it.