We were on Harmony in November, but didn't have our grandkids with us this trip. There is plenty of free things for a 10 year old to do. They do have Adventure Ocean (I think that is the name on Royal) for kids that is free too. There is no charge unless you leave them past a certain time.
We took our 5 grandkids on Liberty in June (ages 17-8) None of them wanted to go to the kids area. They spent their time hanging out with us or their parents in the evenings. The sports courts are open, mini golf, ping pong, getting pizza or just hanging out in the room. Plenty to do on all the ships to keep kids busy. They were so tired after all the day activities, keeping them entertained at night wasn't a problem!