We've been to St. Maarten with friends who have time share, three times in the last three years, for two weeks each time. Renting a car and driving is easy and should give you the flexibility you want. Beware of crazy drivers and heavy traffic. Head back to the ship with plenty of time (at least an hour) or you could get stuck in traffic. Otherwise, don't leave any valuables in the car when you park it, even if you lock it up. Break-ins are not unusual. It's only two-lane highways and driving at low speeds. Exercise caution and you should be fine.
Highlights for us were (heading left towards Simpson's Bay) the Sunset Beach Bar, at Maho Beach at the end of the airport runway (planes flying low overhead), Marigot market (French side), Grand Case (maybe lunch, chicken & ribs at the LoLo's in Grand Case (Talk of the Town), or Grand Case Beach Club (lunch and swimming), Orient Beach (nice waves, great beach), and circle around the rest of the island back to Philipsburg (best duty-free shopping in the Caribbean, I think). St. Maarten is busy and fun.