Another way to do this is to use a device to find the hotel’s DNS servers.

record those on a paper.

Power up your router, connect laptop to it, and go in and manually specify the DNS servers to use, i think by default on my GL-AR750 they were set to Google DNS.

Once you change the DNS settings to the hotel’s dns servers you can try to hit google or whatever else, and you will be redirected to the hotels splash page where you can authenticate, at that point the hotels DNS will allow you to get to whatever you want (or you can establish your VPN connectivity)