Your dining rotation should be printed on your Key to the World Card (room key). On our 7-day cruise, it looked like this:
LAPLAPL
L being Lumière's, A for Animator's Palate, P for Parrot Cay. I would imagine it would have a T for Triton's instead of the L, so it might look like this:
TAPP
I think that you eat at the same restaurant on the third and fourth nights, but I'm not positive about that. In any case, if you don't want to miss any of the restaurants and can't get Palo reservations for the repeat night, you can make your reservations for Palo early, and then go to the dining room for an appetizer or a drink just to experience it.