Personally, I would pick Anguilla over St. Barts and especially in your case.
The boat ride may lull your son to sleep. If you go out of Simpson Bay, while more convenient, it is substantially more expensive. We have used GB Express on past trips but you will pay about double the public ferry price. While we like GB Express, you will get more of a "local feel" with taking the public ferry from Marigot.
Regardless of where you depart from, take your passports as pat said and DO NOT leave anything of value in your parked car. This goes for ALL places on the island.
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