The Half Fare Card and the Swiss Family Card are valid as far as to the border station, being Buchs SG, St. Margrethen, or St. Gallen depending on the connection you will take.
You can declare these reduction cards while booking a through ticket, they are accountable for the Swiss stretch. Alternatively, you can split the journey and book a ticket for the Eurocity train only, from the station where it leaves Switzerland, and a ½ fare ticket for you for the travel from St. Moritz to this station. Your child will travel for free.
The booking is possible through Deutsche Bahn (https://int.bahn.de/en), or SBB (https://www.sbb.ch/en)
Let us know should you have more queries.