The air admittance valve helps air enter your drain line so as not to create a vacuum condition, when it is to far from a normal roof vent. It also has a spring loaded flapper that closes and will not let gasses back into the RV. If you can access the valve they normally screw off or out of the connecting pipe. I would remove this and see if the problem is still there.
I tend to think though, that this is going to be a tank vent problem. When water flows into the tank it will displace air which is pushed up and out the roof vent. When you are pulling the gray tank valve you are allowing the tank to breath and get rid of the excess air, which is allowing it to drain.
Many people have found wasp nest under the roof tank caps that have caused issues. While it is unlikely the vent may be clogged by waste from the tank and may need flushed to clear it.
Let us know how things go.