No, you cannot change the drive mode for a family member's trip in your app. The app sends trip information based on the mode your family member selected before starting the trip. Even if the mode is changed afterward, it won’t update in your app once the trip is completed. We’re actively working on a solution for this in future releases.
Your family member can change the Driver/Rider mode for their trip. For step-by-step instructions, please refer to this FAQ: How Can I Change Driver or Rider Mode?