On all the cruises I have been on (12) children have been allowed at all of the shows at night time. Some cruise lines ask that children don't sit on the front row, but usually they are encouraged to go as on some nights they have magic shows etc. The shows aren't usually that long that the children get bored but you will have a good idea of the type of entertainment from the cruise newsletter which is delivered to your cabin daily. As long as they aren't too young I'm sure they will love it.
Hi, yes they can. Our children have enjoyed the shows. In the Daily paper provided on ship you will be able to gauge if the act is unsuitable. Our kids love cruising on board P&O Oceana - if this is same ship as you are going o.