Margaritaville. Showers, washrooms, lockers, loungers, LIFEGUARDS. No requirement to spend anything, unless you want to.
The Margaritaville bus will pick you up around 10 or 11 at your cliff or beach resort and drop you off around 4:30 if you want to go that route.
Be sure to tip the driver. If your resort doesn't offer free beach transfers; have them call Margaritaville for you to be picked up.
No it's not very Jamaican; but it employs lots of Jamaican people and it's kid friendly.