The Sunset Beach Bar on the beach at the end of the runway at Juliana airport is definitely still open, as I enjoyed a burger and a couple of beers there last week while watching the big planes come in. Actually, one week ago today!
The little beach is open and fully accessible, too. There are warning signs around telling that the blasts from the planes can be strong and could cause damage. The bar itself is not DIRECTLY under the flight path, but slightly offset. I wouldn't worry much about that.
The roads there are... interesting. Small, and people tend to stop in the middle of the road to visit a lot. The taxis will typically be along the lines of a Toyota Corolla (anything larger is pretty rare). Getting taxis is pretty easy.
Not sure what the carseat question really is, but I wouldn't expect the taxis to provide them. If you have them, and there's room in a car about that size, I'd imagine that they'd let you use them.
The reason the other poster didn't post the link is that it's pretty common to find topless women on all the beaches on Sint Maarten/St. Martin, and I believe that topless women drink free at the Sunset Beach Bar, although there were no topless women drinking there the day we were there. There were a few on the beach, just a few steps away from the bar. The kids probably won't notice, can't speak for your DH, though.
Here's a page with some awesome photos of planes coming into the airport. Lots of them are taken from the Sunset Beach Bar. (I haven't spotted any "objectionable" content in these photos.)
Planes landing at Maho Beach/Juliana Airport
DH and I loved sitting and watching the planes come in, so low you feel like you could almost touch them from the sand! They have a chalkboard where they list some of the incoming flights, and they have speakers mounted that are tuned to the air traffic control frequency, so you can actually listen to the tower talking to the pilots as they land.
You should be able to get a taxi from the port to the bar easily, and relatively cheaply (sorry, don't know the price.) It's not far, maybe a 20 minute drive?
The entire island of Sint Maarten/St. Martin is smaller than the area of WDW, just to give you a little perspective.
LOVE that island, and I'm ready to go back (even though I just got home from there in the wee hours of this morning!!!)
