Sometime in the summer when the weather is settled and there are no hurricanes brewing take a trip like this: Ches. Bay to the C & D, to Cape May. Await a wx window and sail direct to Block Island or Buzzards Bay (a two day mini-offshore trip). Then cruise LI Sound, take the East River southbound, lay up at Sandy Hook until you can do a three day coastwise trip non-stop to Norfolk, and then home. In that trip you'll deal with all the stuff you'll need to cruise to the islands and more -- offshore, tides and currents, anchoring up in strange places, provisioning for a long trip, managing the boat systems while out of your home turf. If your target is the Eastern Caribbean, the offshore trip to the islands will be just like the trip from Cape May to Block Island, only longer and quite probably rougher. (I'd leave the kids at home for the offshore bit and let your wife or someone fly them to the boat once you've arrived in the US/BVI.) If it's the Bahamas that are your target, cruising the ICW with your kids should be easy after the training you've done in the Ches. Bay and practice summer cruises to the north. When you get to Florida the passage across the Gulf Stream is no big deal if you pick the right weather.
You should also investigate the Suddenly Alone Seminar that was developed by the Cruising Club of America.
Also have a look at CCA's website where you'll find this:
I'd skip the USCG license courses unless you intend to use the license professionally.
The biggest thing to do is build the confidence of your spouse by letting her do some of the stuff on the CCA checklist under your supervision and without raising your voice above a conversational tone. What the hell, let her be skipper for a day. Pretty soon, you (and she) will be surprised at what she's learned and is compentent and confident in doing.