You may need to ask assistance from the hotel network admin. Big hotel chains may not like that guests bring their own streaming device. Small/independent hotels and guest houses may be more flexible, if streaming doesn’t disrupt internet access for other guests.
Apple TV doesn’t work with networks that require a sign-in with username and password (captive network portal). If it is allowed, you may be able to use a travel router in between their network and your devices, to create a shielded, internet connected, mini-LAN, that has the captive network portal for the travel router, but regular network name + password sign-in for your devices.