I agree with everyone else. One of our children was actually much pickier on the cruise than she usually is at home. We didn't push it too too much as it was clearly situational, and she ate a LOT of mac n cheese and buttered noodles. On her first cruise as a 2 year old she also had grilled cheese for dinner when it was nowhere on the menu.
One thing about ordering off the adult menu though - you need to be clear and up front about what you want. My daughter wanted pork with applesauce, and there was pork on the menu prepared relatively simply. I thought I was clear that she wanted just the pork not the sides, but they brought the whole regular adult entree plus the apple sauce in a separate bowl. She freaked out when they put it in front of her. Once I got a second plate, scraped off the sauce it came with, cut it into a smaller portion, and removed the non-steamed veggies...she was very happy and ate a lot of it.
I also asked our server for steamed broccoli or carrots at every meal even if the kids asked for fries, and often got extra broccoli. At home they eat many more veggies than are available on the ship, but neither of them will eat a veggie in any form other than raw or steamed (..........).
Oh, and there is always plain salmon and plain chicken on the menu.