Also someone please tell me what the best night to reserve Palo would be, also considering we still want to visit each regular restaurant and enjoy those with our children.
This is a hard one to answer, because you don't know your dining rotation or theme nights until you get on the ship. Based off of our last cruise with this itinerary, as for theme nights, semi-formal night was Monday, which was a sea day, and Formal Night was Thursday, then Pirate Night was Wednesday. So, Saturday night (first night), Sunday night, Tuesday Night and Friday Night were cruise casual (so like Khaki pants and short sleeve button up shirt for guys, and like a casual skirt and top, or casual pants and blouse for a girl). we always like to choose our Palo Night for a cruise casual night so we get another excuse to dress up fancy.

But, we like to dress up because we never get to do that here in Seattle (Seattle is a very casual city, so unless it's a holiday party or a wedding, women just don't dress up in formal dresses, or cocktail dresses, etc, and men just don't wear suit out to dinner).
I think that the Captain Gala was on Thursday night (formal night), and they usually serve Lobster in the dining room that night (all dining rooms), but from what I heard, I think on the night they serve lobster in the dining rooms, you can get it in Palo, too... but not sure about that. So, if you LOVE lobster, then try to eat dinner in the dining room on the night of the Captain's Gala. The Captain's Gala is basically where the Captain is around for people to greet him, get pictures with him, as well as all the officers, etc., and like I said, the meal is a bit more special.
But, as for dining room rotations, I agree if you haven't seen Animator's Palate, it's so worth not missing it!! It's very cool. But, you won't find out when you eat there until you get on the ship.
So, what I would do is decide if you want to go to Palo on a semi formal or formal night, so you don't have to dress up more than twice (if you aren't big into dressing up formal), and then book it on either Monday or Thursday evenings. Or, if you are like us, and like to dress up fancy more than twice on the ship, try to book Palo on a cruise casual night, because you have to dress up at Palo... there is a dress code. So, that gives you a 3rd night to dress up really nice.

Of course, this is based off of the assumption that the theme itinerary is the same as our Eastern 7-day cruise last Feb (2010). I would imagine it's still the same... but they can very easily change things, too.
But, if you care the MOST about the dining room rotation and don't want miss certain dining rooms, then what I suggest is booking Palo on a night that sounds good to you, or when there is an opening when you book online, and then as soon as you get on the ship and find your dining room rotation (which will be in your room when you get into your stateroom), then if you find out you booked palo on a night when you'd rather be in the dining room, then you can always try to change your reservations to another day. There almost always are openings (from either cancellations, or people moving reservations to a different day), but also I found out from Palo that they actually keep a few spots open that are not even available online for people who didn't book online but want to just book once they get on the ship...
So, this would be your solution to the dining room rotation.... just change your resrevation with Palo once you get on the ship if you want to be in the dining room the night you booked it online.
But, the suggestion of booking Palo at the opposite time of your seating (so if you have late dining, booking it early like 6 PM), or if you have early dining, booking late like 8:30 PM) works great, too. Then, you can go to Palo, but also go to the dining room, and just not eat, but just go there to enjoy the restaurant and atmosphere of the restaurant.
But, just an FYI if you do that last option.... Palo typically takes a full 2 hours, so if you have a late seating at 8:30, and you want to book Palo before hand in order to still make it to the restaurant to just enjoy the restaurant, book it between 6:00 - 6:30 PM so you can make it to the restaurant by 8:30 PM.
So, these are just my tips....
Kathy