Japanese child travelling to Switzerland with divorced mom with Thai Passport

My girlfriend is coming to visit me for a month in Switzerland and she would like to take her 8 years old daughter. The girl has a Japanese passport which doesn't require any Schengen visa. Her mom has a Thai passport and she received a Visa (I had to make a declaration of sponsorship for ONLY her, as in all the documents we filled it wasn't required any information about travelling with kids). Given the fact that she's a legal guardian of the kid and that she has birth certificate and similar documents to prove it, what kind of problems could arise at the Swiss border once they land?

Thanks.