We took our 3 kids on two NCL cruises when they were the age of your kids - we like NCL as you get a lot of bang for your buck - ie drinks package and some speciality meals included, where as these can cost a lot extra on RCL. They don't have quite as much for kids to do on board as RCL, but still plenty, and my kids LOVED it! There was mini-golf, ropes course, climbing, bowling, arcades, swimming pool and slides, shuffleboard (which was their favourite!), table tennis, sports court, giant chess, trivia quizzes, movies. They were never bored, and they never even made it to the kids clubs.
We went to Grand Cayman, Bahamas, Cozumel and Jamaica on one cruise, and Costa Maya, Cozumel, Roatan and Belize on the other cruise. All were very easy, with plenty to do for the kids.
We had a family ocean view cabin (window, no balcony) for the 5 of us, and it was absolutely fine.