Hi, we were on the Liberty in October. You don't need tickets for the ice show. Like the compass says, the Ice Show is open seating and the doors open 30 minutes prior to the showtime. It runs 45 minutes from start to finish. Try to get there approximately half an hour early though. On our sailing, they had five shows with different times and days, so like MCPayne said, just chose the time that does not conflict with your dinner time.
Also, boarding at 11 is a good idea. We were there around noon and it was a super long line already. So I guess a lot of people came around 10:45 or 11:00. Got to remember to do that on our next cruise!
I can't help you with the Royal Babies activities though because my youngest "baby" just turned sixteen
Have a wonderful cruise!
2006 - Mariner of the Seas
2009 - Independence of the Seas
2010 - Liberty of the Seas
2011 - Navigator of the Seas
2011 - Jewel of the Seas