That carryon rule is a joke. I wish the airlines would start to enforce the carryon size boxes, and count the number of bags people are trying to bring on the aircraft. Some people we have seen abusing the system take there giant carryon bags, and automatically gate check them just before they board the aircraft, saving checked bag fees.
As for useful information, we have traveled many times from Kansas City, mostly on Delta, and SBC, with checked bags. SBC is amazing in SXM. Twice they have put us on earlier SBC flights (once avoiding a transfer from SXM to the Grand Case airport, and this year, just bumping us onto an earlier flight, even going so far as to look for us in the customs line coming off the Delta flight). Once several years ago, the SBC gate agent got us on an earlier WinAir flight (which I don't know if they still do that with the changes in WinAir).
Just as I say that, you will have some kind of delay that stresses your process. Even though we have never used Premium IV in the airport, we know Vincent from a villa we stayed at on the island (he was their concierge), and have used James to help us book cars on the island. They are good people, and I have read nothing but great reports about their services in the SXM airport. It sounds as though engaging their services would make your trip more stress free.
Don't worry about your carryon size. The SBC planes are mostly small, and usually, you just throw your carry on in the back of the passenger cabin. They will weigh it to balance the weight in the small aircraft, but we have never had a problem with being a little overweight on the bags (checked and unchecked) with SBC.
If your son is adventuresome, you might ask if he wants to ride up front in what would be the co-captains seat on the small aircraft. If he is afraid of flying, I would recommend you distract him, by encouraging him to take pictures out the plane side window on the landing in SBH, and sit toward the middle or back of the aircraft.
As to the comment made by Davesmom, I have seen the tables in the departure area of SXM for the big planes, but you don't need to worry about them for the short flight over from SXM to SBH (I haven't seen any tables near the small commuter planes gates). I have only run into the tables being used after going through security one time, and that wasn't in SXM, it was in Mexico.