One fun activity geared to families with kids of (almost) all ages is horseback riding in the rainforest.  It isn't really much of a 'lush' rainforest, but the horses are good and the path easy to go on.  The ride lasts for a couple of hours, with a stop midway through by a creek which enables all weary riders to take a dip in a (very cold) creek.  Kids like it, and parents generally don't go in.  Be prepared with a bathing suit, towels, and definitely sunscreen lotion.  A hat would be a good idea.  Given that it is a rainforest, having a poncho, or basic waterproofing, also makes sense.

The Westin hotel in Puerto Rico can help you arrange all types of activities ( and is a fabulous place to stay for a family (but pricey).