We took my daughter to Negril when she was 9 months old and it was the best decision we could have made. The local were extremely accommodating and we even took her to dinner at Ivans where our waitress gave her a tour of the bar and kitchen.
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Don't worry about the drive, our driver was very accommodating and even stopped in Lucea for us so we could all have lunch. We are going back with her in May (she will be 2 1/2 this trip)