Bonzo: If the hotel has free WiFi (or you pay a daily fee for it), that has nothing to do with your home network (unless trying to remotely connect to something at home and you know how to do that).
The hotel WiFi will likely first redirect you to a website where you give your room number and agree to their terms, or you may need to get the key/password from the front desk.
your Home Hub is your Home Wifi..>
The Hotel has it's own Wifi – (call it their own Home – well Hotel – Hub if you like)
No. You will be using the hotel's WiFi connection not your own.