score:4
If I ask for a refund of the new ticket, are there any laws that I can build my claims on?
Assuming this was booked on separate tickets this is a clear "no". Article 15 of Singapore Airline's contract of carriage clearly states:
... If a Passenger holds more than one ticket and where such separate ticket(s) is not a conjunction ticket issued in connection with the Carrierβs ticket, Carrier shall have no obligations, duties or liabilities, whether to the Passenger or otherwise, in respect of such separate ticket(s) not issued by Carrier.
https://www.singaporeair.com/en_UK/global_footer/conditions-carriage/