When we went in August there was a welcome aboard show, two production shows, the ice show, a farewell show and a couple of "headliner" shows - and - then there are the two parades. We enjoyed all of the entertainment. I hope this helps!
You can check each evening in your cruise compass as to what the next evenings entertainment will be. They usually have different variety acts, musicals, etc.... They should all be Ok for the kids and be sure to catch an ice show, the kids and you will love it.
The production shows are "song and dance" type shows. The headliners can be just about anything but the compass will have a pretty good description so you will know what to expect. It is hard for me to say whether your kids would enjoy them. My daughter would have loved them at those ages but my son would have hated them!
We just returned from our 3/15 cruise on the Explorer, and the shows were fantastic.
The ice show is a must see. They had a group on called Revolution I think it was, that did a Beatles tribute that if you closed your eyes you would think it was actually them.
They have always had great shows( this was our 3rd time on the Explorer).