If there are no other discounts available, you can book any package through your AAA agent and you will get a discount on the room portion of the package. So you can book a MYW package with room, tickets & any of the Dining plans through AAA. If no other promotion is available, you will get 10-20% off the room rate.
BUT if Disney is offering any promotion that works out to more than 20% off the room part of the package then take the Disney promotion. Your AAA agent can still book the package for you with the Disney promotion, but you only get the Disney promotional discount, not the AAA room discount. But there are a few perks you get from booking a Disney package through your AAA agent. These include the AAA diamond parking pass (allows you to park closer to the front gate most days at most parks) and a discount card you can use on Disney merchandise in any
Disney store, as well as a few other things. You will get the same promotions as you see offered on the Disney website.
We currently have the 4/3 deal booked through our AAA agent for our May trip. Your AAA agent can even book you on the Free Dining if it is offered again.
That said, there are some disadvantages to booking through AAA (or any TA for that matter) Any changes you want have to be made through the TA - you can't call Disney direct to make changes. You can make your own dinner reservations if you prefer, though.
And yes, everyone in the room has to be on the same package, and have at least a one day park ticket. (Some exceptions for AP holders & DVC owners I believe.)