Hi. I haven't been on the Liberty, but have been on the Freedom, Liberty's sister ship.
Unfortunately, I don't have kids, so I can't help you there. What I can help you with is the ice skating show.
When I was on my last cruise on the Freedom (October of 2010), tickets were still being issued for the ice skating show. Check your cruise compass for the day and time. It will usually be that first full day. What dinner seating you have depends on what time you can choose. Example, if you have the late seating, then you cannot choose the 9:00 pm time for the ice skating show, as this will conflict with your dinner seating. It is not necessary for everyone in your group to go down to get tickets. Just one person needs to go, and tell them how many tickets you want. Get down there early to maximize the chances of you getting the show time that you want.
2007 - Majesty of the Seas (Bahamas)
2009 - Enchantment of the Seas (Western Caribbean)
2010 - Freedom of the Seas (Western Caribbean)
2013 - Golden Princess (Alaska, roundtrip from Seattle)