How do you create a object that makes a group of players go into a reserved server?

Simple. In the TeleportService There is a function named TeleportToPrivateServer Which people has also used to make free VIP servers in game with commands as well as minigames as like the story games.

If its one player being teleported with a localscript

local Teleportservice = game:GetService("TeleportService")
local player = game.Players.LocalPlayer
local ID = "Remove the quotation marks and put a game ID here"

Teleportservice:TeleportToPrivateServer(player, ID)

If its one player being teleported with a serverscript

local Teleportservice = game:GetService("TeleportService")
local playername = "HeyItzscoop"
local ID = "Remove the quotation marks and put a game ID here"

for i,v in pairs (game.Players:GetChildren()) do
if v.Name == player then
    Teleportservice:TeleportToPrivateServer(v, ID)
end
end

If its a whole party of people with a serverscript

local Teleportservice = game:GetService("TeleportService")
local players = {}
local ID = "Remove the quotation marks and put a game ID here"

for i,v in pairs(players) do
    for i,player in pairs(game.Players:GetChildren()) do
        if player.UserId == v then
            Teleportservice:TeleportToPrivateServer(player, ID)
        end
    end
end

-- Use above for teleporting the party. Use below for adding people to the party in a serverscript (User must use /join to join queue)

game.Players.PlayerAdded:connect(function(Player)
    Player.Chatted:connect(function(message)
        if message == "/join" then
            table.insert(players, Player.UserId)
        end
    end)
end)

get players in a certain area and teleport them or you can just make list of players waiting (table) and teleport them