Hello,
Thank you for provided information.
From provided description, you are connecting to Hotspot network where as you mentioned need to agree with term & conditions which is usually used in Hotspot network. Routers cannot authorize them self in this kind of network (Hotspot network) and because of that, it will not get internet access via WiFi.
Router can only connect to wireless access points aka simple WiFi access points which are not using Hotspot.
Best regards,