I can get my photo booth to require a Facebook like in order to post to a profile. Guess where the software is written? I guess it's an American thing!!
I've not come across this on routers yet myself though. I suspect it could be done via a typical forced browsing page. Most public hotspot routers allow you to set a forced browsing page that opens in your browser regardless of what address you type in until an action - or rule - is performed. For example, you might be able to do a hidden blank page on her website with a simple Facebook "like" button. The rule could be set to then forward them to google.co.uk once the like is performed.
I suspect this is the kind of methodology used, but I've no experience of it and don't know what public hotspot routers would enable this. The only public wifi I have set up is the Gym on Newport Road which is a simple log in page where you are requested to enter a password given by reception. Even this could then be redirected to a hidden "Like" page, but then it couldn't be enforced, only politely requested. As long as the password is entered they could manually browse to any website they wanted.
Good luck in finding a solution, and if you do please let me know.
An alternative (and usually far cheaper) way of spreading likes is a simple competition with a small prize for the winner that is drawn. This got my hot tub hire page almost 300 likes within a couple of weeks. I'm currently deciding what I could offer as a prize for my photo booth page.