Can't speak from personal experience, as our cruise isn't until October, but I have been doing a TON of research about doing Orient Bay on our own. The beach has a number of different "beach clubs" that will rent out chairs/umbrellas for the day for about $20 for two chairs and an umbrella and perhaps a complimentary drink. From my research, it looks like the Kakao or Bikini Beach bar have some of the nicest facilities (restaurant with good food, bathrooms and showers), and the beach chairs are spread out enough so that your kids have room to play in the sand next to you. When you get to the beach, you want to go left (as you're facing the water) to get to these areas. The beach club on the right (club orient) is the clothing optional one. The rest of the clubs on the right may have some topless sunbathers, and nudists might walk down to that area, so just be prepared for that.
If you google "Kakao beach club St. Martin" or the same for bikini beach bar, there are a number of reviews and photos on tripadvisor. I believe you can ask your cab driver to drop you off to one of these specific clubs. As for the return trip, you can either pre-arrange a pick up time with your cab driver, or I have read that the beach club staff can call a cab for you when you are ready to leave. I have also read that cabs are plentiful and waiting to take people back to the ship, but I'm not 100% sure about which way is best.
Hopefully someone with first-hand experience will also be able to provide their two cents, but I hope this was somewhat helpful for you. I would love to hear your experience when you come back and if you can provide some tips! I want to take a cab to orient beach in the morning, head back to the ship for lunch and then, depending on our mood, either stay on the ship while the majority of people are gone for the day, or take a cab out to Marigot for a little shopping.
Have fun!!