3. Go to travel router's admin page (192.168.8.1 or similar)
4. Click buttons and join the Hotel/Cruise/Flight WiFi
5. Go to neverssl.com (or google.com or whatever)
6. See the captive portal of Hotel/Cruise/Flight and follow instructions.
In other words, for the portal, it is no different than using your phone. The extra step is logging into the admin portal and having the router join the public wifi first.