Hi Pettway, we are on St Martin right now having gone through your exact dilemma. We are thrilled to be here rather than in Boston having more snow, but yes, it is different than St Barth of course. We are not trying to recreate St Barth here on a different island but just trying to explore for its own fun and interest. FYI, we have also enjoyed Guadeloupe so may be more adventurous and exploration oriented than some people.
We are staying in Grand Case at a boutique waterfront hotel and have been very happy with our choice, but it's not a family oriented hotel (mostly 1 bed rooms.) But, coincidentally just last night we were saying we would not be comfortable in this town with young kids (ours are now 20+ and not on this trip, but we started going to St Barth when they were 13, 10, 7) simply because there is one narrow road in town with limited sidewalks and lots of fast traffic. Grand Case Beach Club might be good (we stopped by today) because it is self contained so you could let the kids off on their own more. In Grand Case,, during the day the kids could wander a bit on the mile long town beach that has many beach front restaurants to explore and is safe from traffic, assuming they have good sense ocean-wise. At night, we have been warned to not try to walk the beach because of rare, but potential crime, although we just did tonight slightly after sunset and had no issues or concerns.
Yesterday we were hit in Grand Case with Sargasso, but happily today the tide floated it all away. The hotel manager said to not worry and he was right.
St Martin has 20+ beaches so you'll find more than one you'll like. We are also towel on the sand people, not lounge chair with service people, but we had today a truly excellent cerviche in our $10 lounge chairs on Pinel Island, a 5 minute boat ride from shore. Here is a quick story from this afternoon that helps differentiate St Martin from St Barth. We took the tiny 'ferry' to Pinel Island to explore on our own. Conversely, most Americans arrive to Pinel island via 45 minute stops on the day long booze cruise catamarans. You hear their drunken yelling offshore and then they wade into the beach like a zombie invasion. They stagger around instagram posting until called back to their boats. As soon as their apocolypse departs, there is blissful silence, plenty of room on the sand and sea and in unison, all the French women on the beach transitioned back to their traditional beach uniform, which Ironically is probably what the zombies were looking for in the first place. Your goal, should you come, will be to stay away from the ugly Americans, which are plentiful, but also easily avoidable because they travel in large herds that you can hear from miles away grazing on the Dutch side.
Note that the island is at less than 1/2 capacity which makes everything easier, especially for a new visitor because we haven't needed to fight for parking or reservations etc.
Also, there lots of great restaurants of all types, stores and hotels, but there are also mixed in a similar number of dilapidated buildings waiting for rebuild after the hurricane or other trouble. It is not pristine like St Barth, but there is lots of good stuff in the mix. If you have allergic reactions to tumble-down, then it may not be for you, or stay at La Samanna and don't leave the grounds. If you get a sense of excitement seeing a local guy carve a new business from the ruins of an old business, then stay wherever, rent a car and explore.
Sailing, I'm not a kid, but I love taking out the lasers on Gustavia harbor. Looking for something similar before we got here, I found online a Hobie rental place near Orient Bay that gives (requires?) lessons before you can go on your own. I have not tried to visit them yet. Are your kids too young for wind surfing or kite surfing? My wife said I am too old and vetoed that plan, but all of that is available.
Happy to say more if you have specific questions. My comments are just one guy's opinion of course