I think Negril would allow you to move around the beach a bit and participate in some of the daily music jams, etc., while also keeping your child happy. I love that at some places, the staff or owners children are around and your kid can make a local playmate while you enjoy your stay. I know 1 1/2 is young, but that connection could last from year to year. The food choices are plentiful and you'll find something for every member of the family. With a little one, I'd recommend a private transfer over a taxi. I think Negril is a better choice than MoBay every day... so I'm biased!
ETA... not sure of your budget, but I'm thinking about your "sleeping by the crib at 7pm" thing.... Rondel Village has some villas (one, two and three room) available which would give you a little more space to enjoy your evenings but let the baby rest comfortably too... maybe
