Thank you!
Yes the hotel has LAN connections. Then it should work, would you say?

That won't work, unless the hotel had LAN connections and you could then plug a LAN cable into the small WLAN repeater in the hotel room and use it as an access point.

I think it would be better for holidays if you could organise a SIM card from a local provider where you would then have unlimited data and then you could set up a hotspot via phone or use a small 4G LTE router that can then also receive an LTE 4G signal. The Chromecast can then be connected to it.