Air admittance valves on top of the tank vent pipes are a very bad idea. The tanks have to vent as they are being filled. The air admittance valve will allow air into the tanks when dumping, but will restrict liquid from entering the tanks with the dump valves closed.
Your drains will gurgle and flow very slow if at all when the dump valves are closed. If you try filling the grey tanks with the dump valves closed or do any back flushes on them, you very well may rupture a tank or cause a joint to leak especially at the tank connections. You might also cause the rubber flappers to dislodge inside the AAVs on the tank vents or even the ones under the trailer sinks rendering them useless.
With the dump valve closed on the black tank you will get you will get a displacement of tank air into the bathroom every time you flush the toilet. You might also get splashed with tank contents as the tank "burps" into the bathroom.
Vent through the roof, the end gable of the building or go through the wall into the other side of the building and tie into a plumping vent there.