The majority of drinks at the resorts are rum based with different mixers and juices...just ask for a list and start checking them off... don't forget shots of mamajuana! If you stick with all rum based your less likely to get a hangover vs. throwing in tequila/vodka/gin, etc.
Also...try mixing in a few batidas...which are fruit shakes without alcohol...when you find the combos you like (chinola(passion fruit)/mango/fresa(strawberry), etc.)...just have them add some rum and make up your own frozen cocktails
