Welcome to the boards.
There are many differing opinions about the best things to do on any island, but I have been to all of these, and my opinions are:
1. Antigua and St Maarten have the best beaches on your route and I
might use those stops as beach days. There are any number of good snorkling spots and a few dive spots that you can be taken to.
2. St Thomas is primarly a shopping stop. The island is not very
picturesque and the beaches can be crowded. If you are up to a hop
by ferry from Red Hook over to St John, however, the island is well worth visiting. It is nearly uninhabited and has some great beaches.
You can rent a jeep at the S.J. ferry stop and make the loop yourself.
Otherwise, stay in St Thomas and shop til you drop.
3. St Lucia is lovely, but I don't think you could / should drive there. The roads are poor and signage is worse. A ship's excursion is
your best bet for this stop in my opinion.
4. We have been to Barbados several times on both cruises and otherwise. And, I have rented cars there several times. The island's
Atlantic coast is very lovely and can be driven, but the roads are narrow and driving is on the left. Do not go to any of the beaches
on the Atlantic as the surf is very rough and the undertows are fierce.
On the Caribbean side of the island there are lots of good beaches and
several fair dive sites. One of the most common visited ones is a big
German (I think) freighter.
You're visiting a number of good islands. Have a great time!
Ted