any ideas for this part of the trip to St. Lucia??
Any hotels near JFK for the overnight and allow us to park the car for eight nights??

Several of the JFK Airport hotels will do this. We've had friends and acquaintances do this when they fly to SXM on the early flights. Unfortunately, I don't remember which hotels they selected. Go to JFK's website, check out the hotel listings, and call them.

Fellow Albanian

You can try the following:

Park, Sleep & Fly, Park, Stay, & Fly, or Stay 123