You need to book your itinerary/hotel and select credit card payment. Once you have made the booking and get to the check-out page (where you insert the card number) cancel the transaction. (Alternatively contact them directly and they can do the split transaction manually for you).
Your self made booking is in place for about 20 minutes before the robot wipes it away. Contact the support for Future.Travel via the chat link on the website or call them on 24/7 support line via WhatsAp or Viber as soon as you have booked. They will then provide payment links for each credit card to be used and the value to be charged to the card. Example: Mom’s card = $300.00, Dad’s card $300.00, Kids card $1000.00
The tickets are issued after ALL the associated transactions are confirmed. Because it is 1 booking, if ‘Mom’ decides not to go or something else happens and the booking is cancelled, the funds go back to the respective cards.
As a full service agency and OTA, Future.Travel deal with this scenario often for business and family combined itineraries. Most travel agents can do a similar service for you.