Your data stays where it is and continues to be accessed using your own Apple ID. Only the billing and amount of storage available changes. Your current plan will automatically be canceled and refunded when you switch. To change to the Family plan, see the "Switch from your personal iCloud+ plan to your family plan" section of Share iCloud+ with your family - Apple Support including the following:
If a family member is already paying for their own iCloud+ plan, they can choose to switch to your plan or keep their own and still remain part of the family. When they switch to the shared family plan, they get a refund for the remainder of their personal plan. They can't keep their current plan and use the shared family plan at the same time.