Is access to the “Flamingo Island” beach included in the rental?

The private island is called "renaissance island"; on the island are two beaches: Flamingo adults only after 10am and Iguana "family'. If you are staying in the Marina (adult only) Hotel you will get 2 passes and the Ocean Suites will get 4 passes. Basically, whatever occupancy you booked the room for. The passes are included and are good for both check in and check out days. 1 night stay = 2 days at the island if you wish

Yes it’s included with your rental. You get 4 passes for your stay at no extra cost.