Did my taxes, now I need to do another family member. How do I do another tax return of a family member under my account?

When you use online TurboTax software you get one return per fee.

Each return needs its own account and user ID.   If you use the same account and user ID for a second return, the second one overwrites the first return and it is lost forever.  

https://ttlc.intuit.com/community/using-turbotax/help/how-do-i-start-another-return-in-turbotax-online/00/25596