Guess I'm lucky because I've been traveling/flying with my kids from 1 yo through their teens and it hasn't been a PITA.
We prefer Belmar because of the close food options, like Playa Bowls between 8th and 9th. And the boardwalk isn't crazy. Sometimes it's a mixed bag of people over there, but that's never really an issue and you can easily move around if the younger crowd gets too lively. We always find parking a few blocks away, but it may require a few laps around during those prime hours 10-12.
Not sure where 6 people came into the discussion, but you can easily pay $4K-$6K for 4 people (flights, hotel, transfers) in the Caribbean. Everyone has different preferences. I prefer hotels, so I don't have to worry about anything, like cleaning the room, etc. And I prefer eating out at restaurants, rather than cooking, so I want to stay at a hotel near a lot of restaurants.