You are welcome to visit other resorts, dine there, have a cocktail in the lounge, rent recreational items, but sorry, pool hopping is not allowed. Most resorts now ask to see your resort ID, and you will be asked to leave if you are not staying there.
Also, the beaches at some of the resorts are signed that they are for the exclusive use of the guests of taht resort. During the day when no one else is around, it's not a big deal to walk or sit on them, but in busier times such as during fireworks displays they do tend to enforce this rule.
You'll love the AKL, it's incredible!
Anne