Children can and do get away with nice short outfits in the Main dining room on Smart casual nights. Girls even love to wear capri outfits, too. Beach style cutoffs, denim and baggy cargo shorts are definetly not appropriate. Adults should stick to the docker style slacks, dress, or pants suits for ladies for evening. You will see exceptions especially on embarkation night and the last night of the cruise. But, I have also seen this on Princess ships!
We just got off the Sensation and there were two little girls - 2 and 5 - that were adorable and felt very special being served dinner each night. My suggestion would be to make sure you bring them a pretty dress for formal night and take them around to all of the picture backdrops. It's a great way to get a wonderful family photo!!!
When my son was smaller I used to love to dress him in short pant outfits. I think that they are adorable in them. So when people say no shorts even for children I think that depends. Like I said , my son as a toddler, would have looked very formal in his little short pant suit.