I'm not sure I understand correctly. Everyone can go to the island. All you need is money to pay Kapp'n, and the island unlocked.
There are different types of islands.
1. Every town has its own island, which is a part of your save data. This is the island Kapp'n takes you to.
2. There is a online hub island. This is like your personal island, but it's online. You can meet strangers here.
3. There are the minigame island(s). These are for doing minigames hosted by Tortimer, like fishing, bug catching, etc.