Dreams about being trapped on an island often symbolize feelings of isolation or a desire for escape from a situation in your waking life. The small population of people may represent aspects of yourself or relationships that feel stagnant or unsatisfying. The rundown structures and cars could indicate that you feel your current circumstances are in disrepair or not functioning as they should.
Your attempts to swim to the other island suggest a strong desire for change or a longing to reconnect with loved ones, as seen in your letters to your wife and mother. This could reflect feelings of distance, not just physically but emotionally, and a yearning for connection and support.
The fact that no one else is trying to leave the island may indicate that you feel alone in your desire for change or that those around you are content with the current state of affairs, which could make you feel even more isolated.
Consider what aspects of your life you feel trapped in and whether there are ways to communicate your feelings or take steps toward the changes you seek. This dream may be urging you to find ways to break free from your current situation and to seek connections that are meaningful to you.