When my kids were 4, 6 & 8, we did early dinner. The next year when they were 5, 7, 9, we did late. The late dinner was fine, nothing tragic about it, but we preferred the early dinner time we had the previous year. My kids were all hungry by that time and then we had the show afterwards and the whole night of entertainment ahead, including late night snacks as needed. I didn't enjoy having to snack in the 5 pm hour to get us through to dinner. My kids are all early bedtimes (7-8 p.m. Central time) when we are not on a cruise, but we all stayed up until 11 p.m. every night of both cruises because there was so much to do and we were powered on excitement and adrenaline. I would not have predicted that in a million years.
If you like reading trip reports, the one in my signature compares our two cruises in general and your kids are about the same age as mine were on our first cruise. We were also on the Dream. Warning that your youngest may not be up for the shows- Villians Tonight can be really scary and there are some intense moments for younger kids in the others too. On our second cruise, my youngest went to the Oceaneer's Lab and sacked out on a bean bag in front of a movie while we watched the shows. He got a power nap in there and was ready to go to the D Lounge for family fun after we picked him up. Not a great parenting strategy for real life, but it worked on vacation.