Nearly all the hotels on the island are family-friendly. With kids, I think "condotels" or suites hotels are one of the best ways to go. These are not big sprawling condos but usually small lowrise, groups of apartments and suites, offering extra room and a kitchen.
With kids, I also think a pool is a must. So I'd recommend, among others Villas at Banyan Bay, Banana Beach, Paradise Villas, Blue Tang Inn, Caribe Island Resort, Belizean Shores or The Palms.