Magnus...yes...I would spend some time in both the exumas and Abacos (and Eleuthra in between) and not go further south than the T&C until approximately the end of February when the Xmas winds and seas will diminish.
Yes...crossing from West Palm Beach/Lake Worth Inlet is the best way to get to the Abacos. There are TWO options for this passage out of West Palm:
1. Get an early start and cross to West End/Old Bahama Bay and check in and get a slip at the marina. Takes about 10 hours to cross. Next Day negoiate the tricky Indian Cay passage on a 1/2 tide rising and head to Great Sale Cay anchorage 50 miles away on the banks. the first 3 miles of the Indian passage are the worst and you need to be very careful. After that a piece of cake.
2. Leave West Palm Beach Inlet close to midnight. I know...scary! But in good weather, the inlet is WELL lit and wide and easy to exit. This will put you on target to reach the MEMORY ROCK PASSAGE onto the Bahama banks in DAYLIGHT. Memory Rock carries at least 9 feet of water and no worries all the way as you carry on to Great Sale Cay and
anchor in mid afternoon...without checking in to the Bahamas. Just fly your Q flag!
The next morning...head on to the Abacos and check in at Spanish Cay or Green Turtle Cay...and you are IN the Abacos!!
I prefer the second method but the first is more commonly used. Just have good waypoints plugged in from the dodge guide or Explorer chat books for the Indian Cay passage as Nav Aids tend to go missing and there are several turns to make in the first few miles.
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From the Abacos...to get to the Exumas, the easy way is to leave out of Little Harbor and do an overnight sail to Royal Island Eleuthra. From there is is a day sail or two along the Eleuthra bay side to Rock Harbor Eleuthra. A great little place. After that it is another day sail across the tongue of the ocean to the Exumas...(the Land Sea Park is a great stop)....and then on down to Georgetown. All easy.
The Georgetown to T&C route is a bit more open water than your Bahamas cruising to that point will have been, but is not hard as it is nearly south and you can make stops along the way if you need to pull in for weather or just want to visit some of the less trafficked cays and islands. I would stop at Turtle Bay marina on the north side of Provo T&C since you have the whole family aboard. This will be a nice return to USA style ameneties and food shopping before you head south again.
The passage from T&C to the DR is about 24 hours and open water AND hard on the wind. You must wait for the right winds for departure and hold your
line close hauled or you end up in Haiti! Not a difficult passage...but boisterous!
The hardest part of the trip is from the Luperon/puerto Plata area in the DR to Puerto Rico with the Mona Passage crossing. It is 350 or so miles dead into the prevailing winds and seas which are GENERALLY in the 20-25knots on the nose and 6-8 foot seas. During our sojourn in Luperon, we saw numerous boats leave the harbor headed east and limping bak in several hours later finding progress impossible.
I'm sure you've read VanSants book on how to do this...if not, you should. We did not do it his way...we simply waited a long time for a lull and then motorsailed for 3 days. Chris Parker's service was invaluable for this "window" planning. Either way...it is the one part of the trip where you need to be very sure of your boat and your skills as no help is available.
Puerto Rico is great and once there, you can make day hops along the south coast to the VI's without much problem. Turn right at Virgin Gorda and at last the winds will fill your sails on a reach down the island chain.
I have no experience heading from the southern Bahamas to the WESTERN caribe but believe it to consist of longer and more difficult passages due to currents and prevailing winds. Most people use the wind to get down to Trinidad and then have it at their backs as they make their way to the Western caribe...but perhaps someone else here can give a more experienced perspective on this.
Hope the above is helpful to your planning.