Sorry, but that is not how private servers work. They can only be accessed the first time players are teleported to them, and nobody else can teleport to them later. If you want to make this system im afraid you will have to compromise for a party system that teleports them all at once, and cannot be joined later. Good luck!
edit: I was wrong sorry. I looked into it a bit more and found something you might want to look into!
https://developer.roblox.com/en-us/api-reference/function/TeleportService/TeleportAsync