I don't know what you mean by "whole family", but if you're just talking wife and two kids then I would say YES, it is a vacation. If the kids are young, then they can play on the beach all day and you just have to break for naps/snacks. If the kids are older then they won't want anything to do with you so you just have to worry that they are not getting into trouble or giving away their virginity.
If I was to vacation on my own I think I'd still have a ton of fun. I've been to Maui in the past (see under my avatar) and I'd love to go back. If I had a week I'd take a surfing course, dive for turtles or just sit back and enjoy the sun with a cold drink in my hand. I would probably have a difficult time adjusting at first to all my free time, but I don't think it would take me that long.