Influence me – Caribbean trip with baby

Please influence me with ideas for hotels etc and maybe alternate itineraries for a trip I’m planning..

2 weeks flying from London, preferably British airways.
End of November/early December
2 adults and 10 month old. Mother-in-law joining for one week.
Vibe: prefer something that doesn’t feel like Miami – creole/English/french vibe (rum, tea and colourful parasols) and smaller hotels, mother-in-law would prefer more creole feel for week she joins. Potential do do one week more all inclusive and one week in a villa / apartment but would want something ‘serviced’.
Would like to keep budget at around 1000 dollars per night (not including food etc) per room – but probably more like 3000 per night for villa/apartment though. Vibe more little good harbour / cobblers cove than le bartelemy.

Potential routes: week in Barbados then week in one of the grenadines? MIL joining for second half, maybe bequia?
I see Anguilla recommended here a lot, maybe in combination with Antigua/barbuda?
I would love to do Martinique / Guadeloupe etc but connecting through CDG with a baby puts me off.