To get a dining plan, you have to book a package that includes room, park tickets and dining (unless you have an annual pass or are eligible for the military room discount, or are on a DVC reservation booked through member services). And for free dining they must be at least 2 day park tickets for everyone age 3 or over, no exceptions.
A split stay at WDW is considered two separate reservations. On a split stay if you want free dining on both stays, you have to book it separately (one dining plan will not carry over to the second reservation) and you have to buy at least 2 day park tickets with EACH reservation. If you didn't buy tickets with the AOA reservation you would have no dining plan at all covering that stay (except any credits you might have left over the day you check out of CSR and into AOA). You couldn't get free dining for a 2 night stay anyway, as free dining packages must be at least three nights.
Since you are only staying 2 nights at AOA, book enough tickets with your package at CSR to cover your full stay, save enough credits to use for the meals you want on the transition day, book a room only reservation at AOA and pay OOP for food for your final night at WDW.