All these ports are safe.
Phillipsburg St Martins is dominated by the hustle and bustle of shopping. If that's what you want to do then head there. Your family might like Dawn Beach. It attracts locals, condo dwellers and some ship passengers but no where near as many as say Orient Beach . There are chair rentals, a restaurant/bar, more "rustic" tent selling food and drink, VERY friendly vendors (not at all aggressive), and beach is quite nice. Many local families use this beach.
Barbados is a very safe island. There are very many beach choices and several nice snorkelling excursions are usually offered. Bridgetown is not an all tourist town and will remind you more of a small local city. For my money you can skip the town itself.
The best shopping is in the stores right inside the pier and in the little local market place just outside the terminal.
Martinique- The town will remind a bit of the architecture of New Orleans. Lots of shopping downtown and many beach and water sports choices. (some beaches may be topless, this is a french island afterall).
Nice ports have fun.