You could get it a lot cheaper than that.
But if you hired a private driver for just you and your wife, then yes you would probably pay around that.
But there are tons of tour companies that offer that trip for much less. Perhaps Jamaica Tours? Let me see if I can find any that quote a price for that trip. It will be a long day though, it is about a 4 hour trip to Kingston, and of course then a 4 hour trip back. You would be at the museum for AT LEAST an hour, so that is a full day, and of course you would probably want to get out and take pictures, like on bamboo road or even stop in middle quarters to get peppered shrimp, so it would be a long full day for sure. But fun!