It sounds like the problem may be with the flashing (or lack thereof) around your sliding glass door. Flashing is a protective sealing membrane designed to protect a wall at its most vulnerable points, namely where window and door openings exist. In your case, I recommend a flexible product such as Grace Vycor Plus Self-Adhered Flashing, which is designed to work in severe weather climates such as the coastal area where you live. It's compatible with wood, plywood, concrete and masonry, and fully adheres to the substrate to prevent water from passing through.
Grace VYCORners should also be part of your plan: they're prefabricated flashing corners made to work with the flashing product for protection against leaks, and make the overall installation faster and easier.
Note that if the sliding glass door leak you described has already worked its way under any adjacent exterior siding, you'll likely have to remove and reapply that siding in order to install the new material, but the extra effort will be well worth it the next time coastal winds blow rain your way.