Sandals recommended as a luxury resort - hardly - from what I've read and seen - more like Butlins (UK based posters will know what I mean) in the Caribbean.

Carlisle Bay could well have toddlers/babies as it's where a lot of well off young families go from the UK. On the other hand, although The Jalousie Plantation in St Lucia gets families during school holiday times I don't think there'll be many in November. UK half term is the second half of October so no UK families - when are North American school holidays? Should come within budget if there's an offers - like stay 4 get one free etc. and it should fit the rest of your criteria - stunning location right between the Pitons, great snorkelling right off the beach, etc.