You could create a new user account on the same computer.Your family member can create his/her own catalog and Protect the account/data with a password.
This way you can save your Lightroom Activation count and you both can work independently (but not together).
I want them to have the possibilty to have their own private folders on seperate logins?
I don't think it is Possible.If using Lightroom CC/6. You need to share your Login details.You will have to buy additional License in this case.