@Lee337 

Just to confirm, are you able to access the internet when you connect your computer directly to that public Wi-Fi? Do you need to do any set up on the computer?

As far as I know, some public Wi-Fi or hotel portal network may require users to pass the portal authentication before surfing the internet, there should be no issue connecting to the internet when adding a wireless router to it as long as the authentication popup window shows up.

You may try to refer to the below instructions to configure the WR902AC as the Share Hotspot mode:
https://www.tp-link.com/support/faq/1501/

However, if the hotel wireless network requires another login username and password, this WR902AC may not be compatible with that kind of wireless, which may have special requirements or limitations.