Since it's only 3 nights, you'll dine in each dining room once. There is just one rotation: 123. The specific order of the rotation is Enchanted Garden, followed by Royal (Court/Palace), followed by Animator's Palate.
What ever room you start in is #1, so the "rotations" are
ERA
RAE
AER
You can call DCL and place a request for a specific rotation.
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