Air admittance valve is used to keep 'P' traps from getting sucked dry while dump grey waste tank.
You could remove it, cap the stub pipe off and still be able to properly drain the grey waste tank due to tank being vented to roof. Water in 'P' traps could be sucked out but tank will still drain.
When they fail it is that they fail to close allowing odors from grey tank into inside of rig.
If Kitchen sink is only grey that is backing up/don't draining (shower/bathroom sink OK) then must be a 'galley' tank that is FULL.
HEY OP.........
Did you find a dump valve inside wheel well, behind rear wheel, inside a different rearward compartment????