Always the account the family plan belongs to is the admin account. 
If you like to change the admin imo the only way is canceling family plan and resubscribing with the account that is assigned for becoming admin account. 
On canceling the active plan existing family profiles (without own account) will become real free accounts with personal log in data, but you have to do this manually for each profile. After the new admin account subscribed for family plan it can reinvite the other accounts.