RDP won't work as you need a public static IP that the hotel won't give you. I've used this application for years:
https://www.logmein.com
You have to install it on the laptop as a server, then you will be able to connect to it. They have a mobile app and a browser client, so you can use your own mobile phone/tablet to interact with it.
It is essentially like having your own VPS on your laptop.