Hello Spen
Welcome to the SBB Community, a customer support forum run by volunteers.
For mountain excursions it is advisable to check the operator’s website as not all cable car operators do accept the Swiss Family Card / Junior Card / Co-Traveler Card.
As for your question, yes the Swiss Family Card is recognised for free travel by Gornergrat railways and Grindelwald-First. You have to get a free admission ticket at the ticket window in order for your child to pass the turnstiles.
Kind regards,
Roland