Run the 2" vanity drain and connect to the 2" shower (after the shower trap) then connect from there into the 3" line. This will wet vent the entire bathroom. In your current drawing, the shower is not vented.
A real vent (thru the roof) would be better, but I understand the limitations with the vanity placement. Is it possible to flip positions of the vanity with the shower and/or toilet? That may allow you to run a real vent. Otherwise, the AAV should be okay assuming they are allowed in your area (some states don't allow them, but they are still sold in the stores).